It sounds like you both have some difficulties and the environment between you isn't generating good wellbeing for you both.
For you, congratulations on coming out and being comfortable and confident in yourself and who you are; who you know you are really in your heart. Depending on your age, you may have to wait before you can legally change your name yourself. If your mother has problems using your preferred pronouns or name, that is her problem, _not_ yours. Hopefully she will be able to accept you for who you really are.
There are trans specific threads here and support groups you can contact to talk to about the sorts of things that other trans people have gone through with their families. Finding peer support is a good idea.
If you are concerned about your mothers drinking and the impact it is having on your relationship with her, ideally you can try talking with her about it when she is sober. However, if you are not comfortable with doing this alone, it might be an idea to have a friend or other family member (dad, uncle, nanna, etc.) to have a chat with her about it. Other options are to get in touch with one of the support groups for the children of alcoholics, google is your friend on this, to see what other ideas there might be for you to try.
If things are getting actively hostile, you can contact Beyond Blue support line among many other services for information on options available to you based on your location and age.
If you have genuine fear of harm/abuse, the police can and be called.
Hopefully some of that is useful for you,