I have a lot of experience in this area, I checked my former roommate into detox and he is a self admitted alcoholic now and been sober since the day I took him in. A girlfriend of mine has similar problems with cutting etc and even tried to commit suicide. She also had a problem drinking until she blacks out. I have had many long talks with her and she is not an alcoholic in the traditional sense but uses alcohol to deal with the issues from her mental health problems. However, after a lot of soul searching, she's realized alcohol just makes her other issues worse or even magnified and so she's been forced to give it up. My advice would be to have a lot of honest conversations with yourself and others and ask if alcohol is helping or hurting. If it's hurting, why bother trying to label yourself one way or the other, just stop.