I've been in a mental hospital before, and I'm not crazy. Well my family drove me crazy, that's all. But the unfortunate thing(s) about mental hospitals are:
1) It's sort of like prison, very confining;
2) Other people there can be kind of scary;
3) Even if you're happier there, you can't stay there forever. You will eventually have to go home, or go somewhere else anyway.
I'm sorry that your family situation is rotten. You might consider becoming passionately involved in a church with all your heart, mind, and soul. That can cure anything, it may take years to see an improvement in your life, but church is wonderful.