Can you see your high school guidance counselor? You might also want to go to an Al-Anon meeting just to have some type of support for the issue of living with an alcoholic (I know from experience what that's like).
If you don't want to tell your mom about needing a mental health clinician (because you are on her insurance) check with your local health department. There is usually a place that you can go that is free of charge; the ADAM (sp?) board controls it.
Have you done an internet search on cutting? I had a student that did it this year and I learned so much about it online.
Please stop hurting yourself.