Gretchen, but Squeaky never allows doubt to creep into her conversation. If anything, she is cocky and prideful about what she expects to happen.

While all of this may be true, Squeaky also feels the need to prove herself. She works on her running constantly, and she is not afraid to let anyone see that she is doing it. She has to to work very hard to be what she claims to be, and that is a kind of inner conflict. Even her name in this story is an indication of that. While she embraces the name Squeaky most of the time, when she gets ready to run the race, she insists that Mr. Pearson write her name down as Hazel Elizabeth Deborah Parker, indicating a rather conflicted view of herself.

It is also true that Squeaky is in conflict with other people, primarily the other girls in her class who try to hide the fact that they have to work to get better at the things they excel at and those who foolishly allow themselves to be dressed up and worry too much about their appearances and what others think of them. This is a conflict, but this conflict is not resolved by the end of the story.

It is also true that Squeaky has a bit of a conflict with Gretchen because she is the next-fastest runner; however, Squeaky is mostly dismissive of her throughout most of the story.

The conflict which does seem to have some resolution is the one within Squeaky--I mean Hazel Elizabeth Deborah Parker. When she sees her mentally challenged brother running next to her during the race, she comes to the realization that 

if I’ve lost this race, or if me and Gretchen tied, or even if I’ve won, I can always retire as a runner and begin a whole new career as a coach with Raymond as my champion.

She discovers that she does not have to win a race to be successful, a kind of resolution to her internal conflict. Of course, she suggests she could become an expert speller or piano player if she did not keep working on her running, but she has at least realized that life without this particular expression of herself is possible. She has grown and learned something more about herself.

In truth, this is not a always terrible internal conflict for a young person who wants to become something in life, this tension between knowing who one is and needing to prove oneself to the world. In any case, we have little doubt that Hazel Elizabeth Deborah Parker will be successful at whatever she chooses to do in her life.

The main conflict of “Raymond’s Run” is the conflict between Raymond’s sister, the story’s narrator, and society. This relatively young girl, who is called Squeaky but whose name is Hazel Elizabeth Deborah Parker, has the responsibility of taking care of her older brother, Raymond, who appears to have some kind of developmental disability. She says that he “needs looking after cause he’s not quite right.” He is very childlike, and Hazel describes him as having an especially large head, something that many people who make fun of him for.

Hazel defends Raymond against those people who would be mean to him, steal his allowance, or otherwise bully him. She claims that she will just “knock you down and take [her] chances even if [she is] a little girl with skinny arms and a squeaky voice.” Hazel is also pitted against other girls like Cynthia Procter, a schoolmate who seems to compete with her by showing off every chance she gets. Hazel even describes the way her own mother will pretend not to be with her as they walk down the street, embarrassed as she is by Hazel’s attempts to strengthen her knees and lungs so that she can be a faster, better runner. Hazel’s mom wishes she would be more feminine and participate in the maypole dancing rather than the May Day races, hoping her daughter would “act like a girl for a change.” Even Mr. Pearson, who manages the race, tries to encourage Hazel to lose the race on purpose to give Gretchen, another runner, a chance to win for once.

In short, Hazel is opposed by just about everyone in her society, often for her not being girlish or feminine enough. She recognizes that there is something wrong with the way society teaches girls to compete with one another or to act toward each other, saying, “I’m thinking that girls never really smile at each other because they don’t know how and don’t want to know how and there’s probably no one to teach us how, because grown-up girls don’t know either.” She doesn’t want to be a “strawberry” in a play or dance around a May pole in a frilly dress but, rather, to do something that feels meaningful to her (like running fast or caring for her brother) “something honest and worthy of respect . . . like being people.” For this reason, the main conflict is arguably in the story is between Hazel and her society.

The climax of a story is the moment of the most tension between the protagonist and the antagonist, and the antagonist in the story is Squeaky's society. It is this society that tells her that she should be more "feminine," with her mother wishing she'd wear a frilly white dress and dance around the maypole rather than run in the May Day race; with Mr. Pearson asking her to purposely lose the race and give another girl a chance to win; and with the expectation that she play the role of a "fairy or a flower" rather than be herself. It is also a society from whom she must defend her disabled brother, Raymond.

After her race, Squeaky knows that she has "won again and everybody on 151st Street can walk tall for another year." However, there is some contention among the men who are supposed to announce the winner. Mr. Pearson, who'd previously asked Squeaky to lose the race to give another girl an opportunity to win, now seems to be arguing about who has won with the other men on the microphone. All the voices are "mixed up," and Squeaky and the other girl in contention are now "wondering just who did win," though Squeaky had seemed so sure before.

This moment, when Squeaky waits to hear if she's going to be declared the race's winner by Mr. Pearson (a representative of the society that antagonizes her), is the story's climax.

The climax of Toni Bambara's "Raymond's Run" occurs with the action described in the title. As Hazel Elizabeth Deborah Parker races during the May Day race, she glances to the other side of the fence and sees her brother Raymond speeding along with his arms at his side and the palms of his hands tucked up behind him, and she is stunned.

[i]t’s the first time I ever saw that and I almost stop to watch my brother Raymond on his first run.

Squeaky's remark on Raymond's running indicates how thrilled she is with her brother's ability. His style is unique, and his speed incredible. Fortunately, Squeaky catches herself in time and rushes past the white ribbon to win first place. Although she jumps up and down, Squeaky is more excited about Raymond's run. She notes that the crowd must think that she is thrilled about her win rather than about her brother's amazing accomplishment. As Raymond climbs over the fence, Squeaky grows even more excited,

By the time he comes over I’m jumping up and down so glad to see him—my brother Raymond, a great runner in the family tradition.

After realizing Raymond can also run swiftly, Squeaky considers the idea of being his coach. No longer focused on her own running, Squeaky looks at Gretchen, who smiles and recognizes Squeaky as the winner. Squeaky returns the respect, realizing Gretchen can help her coach Raymond.

We stand there with this big smile of respect between us. It’s about as real a smile as girls can do for each other.

Squeaky's consideration for her brother Raymond's talent at the climax of the story leads to her resolution to ask Gretchen to help her train Raymond. Truly, Hazel Elizabeth Deborah Parker matures from her experiences on May Day.

The main character and narrator in Toni Cade Bambara's "Raymond's Run" is the African American girl Hazel Elizabeth Deborah Parker, who, because of her high voice, is mostly referred to in the story as Squeaky. Squeaky is a strong, spirited person who says, "all I have to do in life is mind my brother Raymond."

Raymond is her older, mentally challenged brother who is often "subject to fits of fantasy." She often feels the need to protect him from what she calls "smart mouths." At one point, she tells a couple of girls, "you got anything to say to my brother, you say it to me."

The story is based around a fifty-yard sprint, in which Squeaky races against among others, including the third major character in the story, Gretchen. At first, Squeaky dislikes Gretchen, who she says is new to the area, but Gretchen pushes Squeaky so close in the race that she wins Squeaky's respect. At the end of the story, Squeaky wonders if Gretchen would "like to help me coach Raymond; she obviously is serious about running, as any fool can see."

I would say that a conflict central to the story is Hazel's (Squeaky) internal conflict of identity.  She thinks of herself as a strong runner.  It's how she identifies herself.  She is so adamant about this identity that she limits areas of potential social growth.  For example, she only attends the May Day celebration to run the race.  She won't even consider doing the maypole dancing. The running identity is a conflict because it consumes her.  She puts a lot of pressure on herself to continually maintain her reputation as a good runner.   That pressure brings up another conflict.  Anybody who might challenge her dominance is seen as an enemy.  Someone to be beaten.  That's the case with Gretchen.  Hazel never even considers that Gretchen might be a friend and running partner.  That kind of attitude will lead to a lonely life, so it's good to see that by the end of the story, Hazel's attitude has really begun to change. 

"if I’ve lost this race, or if me and Gretchen tied, or even if I’ve won, I can always retire as a runner and begin a whole new career as a coach with Raymond as my champion."