Is my mom an alcoholic?

Yes, your mother is an alcoholic. It shows a lot of maturity to pick up on your mother's problem with alcohol. That being said, this isn't your fight. Your father should be stepping up to the plate and protecting you from your mother's anger. Have a talk with your dad and tell him how your mother's behavior towards you has affected you. He may not be aware of it. Your mother needs to hit rock bottom before she'll admit she has a problem but she'll need some help getting there. Ask your dad about moving out of the house. If he refuses to go then make arrangements for yourself to live with relatives for a while (with your parent's consent). The sooner you get out of this situation the better. Good luck.