Natural consequences are a good thing for alcoholics to have to deal with.
If she is used to you 'taking care of things' because she is too drunk too, she will lash out at you when you stop. But maybe you should stop? Get involved in some social activities. Join a church, book club, exercise group, study group (or anything else that interests you).
Connect with others and get out of the house. She and your Dad will have to fend for themselves when you are not around and you won't have to be around to deal with the abuse they will likely want to direct at you (although you don't deserve it).
Do it not to try and 'fix her' (you can't). Do it to bring yourself some sanity. Do it to learn that some people will appreciate you for who you are, not what you have to offer (domestic service, sex, ect). You deserve to be happy. The earlier you break away from the crazy making at home the easier it will be to find. Know that you are a magnet for abusive people right now. They have some sort of spidey sense and can pick us ACA people out of a crowd. I swear. I've been a magnet for them my whole life, and I'm a guy. I can't imagine what it's like for a girl. Participate in your chosen activities, but be wary of anyone who 'comes on strong' (not just sexually, anyone who just seems to cling to you like glue).
You asked if you 'caused' her problem with your actions. I'll reverse that. Where was she when you started dating this guy? Did your parents check him out? Did they warn you in a loving and caring way? Where they approachable when he hurt you? Where they available to console you? Did they notice the cutting and try to get you help?
I'm not saying they caused your behavior. You control you, nobody else. But parents are supposed to be their for us. To teach us, to give us tools to cope. Unfortunately for us, our parents were not able to. So, we must learn for ourselves. The trick is to identify what works and leads to happiness and cherish it, and to eliminate quickly those dysfunctional things that we learned to survive in the alcoholic home and delete them from our inventory. If you have done some things that you are not proud of, forgive yourself. Learn how to keep from repeating that mistake. Hold your head high and keep on living your life.