"Do you think she has an organic mental illness, or was her breakdown more psychological?

My Azula's is both, and is affected by both psychological and physical things. (Not always in the way her doctors think.) But then I'm me, so she learns to live with it and does Awesome Things While Mad. (The word she prefers: being "sick" or "ill" is, like, a state of perpetual failure. She cannot have that). Which is kind of hard, considering that healing powers exist. But I DON'T CARE.