He certainly was known to be a drinker, a carouser and a womanizer. By today's standards he would probably be labeled an alcoholic.
Also, by today's standards, Poe would have been considered a pedophile. If you know the real story of Anabel Lee, you'll know what I'm talking about. Back in the day, people might have said, that Poe "liked them young" but 14 or 15 years old wasn't necessarily considered to be too young if the parents consented. (The real "Anabel Lee's" parents didn't consent.)
Poe might have been all that and more but he wasn't "schizo."
Poe was a writer and he wrote to make money. He wrote what sold and, in that time, nobody else was writing stories or poems of such horror and gore as Poe. Poe simply wrote what made him the most money.
What about Stephen King? Do we call him "schizo" because he writes horror stories?
Yes, there are people who have met King who say he often acts pretty creepy but he usually counters by saying it's all an act.
Maybe King is a creepy guy. Does it really matter? Could it possibly be because we want to believe he's creepy?
The same thing goes for Poe. Does it really matter? Could it possibly be because we want to believe he's crazy, too?
In either case, both of them probably played up to the stereotype for "marketing purposes," as it were but I don't think either of them were crazy just because they wrote horror stories. They both did it to make money, plain and simple.
In Carroll's case, maybe he got a little "too close for comfort" but I think it was more out of naivety rather than neurosis.
I think he might have been playing up to his stereotype as a "children's writer," just as King and Poe played up to their stereotypes, but didn't realize the connotations that came of his relationship with the real Alice and/or other children.
I would put Lewis Carrol in the class with the others: Creepy but probably not crazy.