The primary conflict in "Raymond's Run" by Toni Cade Bambara, is an internal one. The protagonist, Squeaky, is trying to figure out who she is. While she acts and talks quite confidently, she constantly feels as if she must prove herself to the world.
Squeaky narrates this story, and she describes herself this way:
There is no track meet that I don’t win the first-place medal. I used to win the twenty-yard dash when I was a little kid in kindergarten. Nowadays, it’s the fifty-yard dash. And tomorrow I’m subject to run the quarter-meter relay all by myself and come in first, second, and third. The big kids call me Mercury cause I’m the swiftest thing in the neighborhood. Everybody knows that....
Later she calls herself "Miss Quicksilver," confident that she will once again win this upcoming race. She talks with and about her greatest rival, 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.