There are two major characters in "Sonny's Blues," Sonny and Sonny's older brother. Each of these characters has an independent conflict and together they share another conflict. Sonny's conflict has multiple parts: heroin addiction; the "vivid, killing streets;" his choice for jazz and blues music over classical, which translates to a choice for poverty and limits to opportunity and freedom and a rejection of an established place in society with at least some economic opportunity, such as his brother attained.
His brother's conflict is what to do to help Sonny. He feels estranged by the seven year age difference that separates him from Sonny. He feels like Sonny's choice of jazz and blues was a mistake and "beneath" him. He feels he failed his mother because she required a promise that as the older brother he would always take care of Sonny...trouble is, he has never known how to help Sonny.
Their shared conflict is how to extricate themselves from the suffering of their racially impeded lives. Sonny has fallen deeper and deeper into suffering. His brother has extricated himself from the suffering in large part--though not entirely--and each still wears the shackles of the suffering from their childhood and youth.
In James Baldwin's "Sonny's Blues," the main character is not the one mentioned in the title, Sonny, but his unnamed brother, who is also the narrator. The narrator and Sonny grew up in Harlem and struggled with inner-city life and poverty. However, they have dealt with their struggles differently. The narrator is now a teacher, a man with a full-time job helping others, as well as a wife and children. He has risen above his difficulties and become successful. Sonny, on the other hand, has gotten involved with the wrong activities and people and has recently been arrested for selling heroin. It seems that the narrator has difficulty expressing his feelings and would rather avoid emotional situations. This may be a part of how he has grown up to defy his surroundings and refuse to let the harsh realities of the community bring him down. His internal conflict is that he loves and wants to protect his brother and therefore cannot fully push away the crime and drug use that surrounds him. He wants to reach out to Sonny but must find the emotional capacity to do so. This is one of the major character conflicts in the story.