A protagonist is the main focus of the story. While in many works of fiction, the protagonist is the hero or inherently good, this does not always have to be the case.
The antagonist is the opposition to the protagonist.
In this story the protagonist is Brother. He is both the narrator and character. We are not told his real name, just that Doodle calls him Brother. Brother is ashamed of his crippled brother, and does not want to be embarrassed by him. He does love him, but does not think about anything other than his challenges. Brother pushes him to walk, then run, and this eventually kills him from the strain.
Brother is heartbroken by the death, and finally realizes that Doodle was a miracle.
At first, it would seem that Doodle is the antagonist to Brother. He causes Brother a lot of unease and trouble. Brother wanted a brother that could do the things all boys can, and was a constant embarrassment.
However, after Doodle's death, it can be seen that Brother was his own antagonist. He was unable or unwilling to see Doodle's wonderful qualities until after he had died.
Brother is probably the principle protagonist, although we only know his name from the point of view of Doodle, his handicapped brother, who also is important in the story. Doodle might be considered a secondary protagonist, and if he is, then his antagonist would be the forces of nature responsible for his misfortune. If we consider Brother the protagonist, on the other hand, the unfortunate Doodle is his antagonist because it is against him that Brother must over come his shortcomings and learn a greater lesson in life—about Doodle.