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."