There are two main types of conflict, internal conflict (man verses himself) and external conflict (man verses man, nature, and supernatural). Internal conflict tends to be the result of one's internal struggle regarding his or her morality and desires. External conflict exists as the result of one conflicting with outside forces (another person/group, natural forces (such as animals or the weather), or the supernatural (such as gods, demons, ghosts, or goblins).
As for the conflict depicted in Toni Cade Bambara's "Raymond's Run," the protagonist (Hazel Elizabeth Deborah Parker, or Squeaky) faces both internal and external conflict.
One internal conflict Squeaky faces exists is taking care of her brother ("All I have to do in life is mind my brother Raymond, which is enough."). Squeaky does not have to do housework, hustle money, or anything else. All she is responsible for is taking care of Raymond. By stating that taking care of Raymond "is enough," one can infer (make an educated guess) that she feels conflicted about it. Her exasperation is evident.
Externally, Squeaky's conflict lies in beating Gretchen in the May Day race. Gretchen is Squeaky's only competition, and Squeaky cannot lose to her. Beating Gretchen actually exists as both an internal and external conflict. Externally, Squeaky must run faster than Gretchen. Internally, Squeaky will not feel as if she is "the best" if she loses.
One of the conflicts in "Raymond's Run" is how Squeaky, the protagonist, will deal with her brother, Raymond, who is developmentally disabled. At first, she tries to help him by essentially challenging anyone who says anything nasty to him. She says, "if anybody has anything to say to Raymond, anything to say about his big head, they have to come by me." By the end of the story, she realizes that the best way she can help Raymond is by being his coach and helping him learn to run, as he has the makings of being a fine runner.
The other conflict is that Squeaky has competition in her race from Gretchen, the new girl. Squeaky at first acts antagonistically towards Gretchen because, as Squeaky says, "girls never really smile at each other because they don’t know how." However, after Gretchen almost ties with Squeaky in the race, Squeaky begins to respect the other girl. Squeaky says, "And I smile. Cause she’s good, no doubt about it." Squeaky is able to form a friendship with Gretchen rather than feel competitive towards her, and she thinks that she and Gretchen might even work together to coach Raymond.