Should I fight for this relationship ?

My girlfriend of about 2 months called me yesterday to break up with me because she thinks that relationship is not working out very well. Apparenlty I'm too serious for her and I seem to be the only one in her circle of friends who realizes she has a drinking problem. Last Friday I nearly broke up with her when we went out because she behaved so inappropriately. She was so so drunk. she's a bit younger than me, and I know at 21 you want to be wild. But I think drinking like that is just unacceptable at any age. To lose a sense of respect for yourself as a woman, and as a person, really makes no sense. She says she loves me, yet she gets drunk out of her mind and treats me like the enemy and embraces her friends. What kind of woman does this kind of thing ? Anyway, afterwards I decided that night that I would leave her and when she realized that, she made a big scene, pushing me and yelling and crying. Completely embared the both of us....That night the girl was so drunk that she had her underwear exposed for the world to see... with her stupid girlfriends just watching on like its nothing. After her crying and telling me that she was sorry I took her back, but nothing has changed.... nothing about her at all has changed. She is still the same selfish and inconsiderate person and while I thought I had forgiven her for Friday, what she did hurt me. I kept waking up and crying at night and in the mornings, with her getting mad everytime I brought it up. Finally we came to a fore with our situation, she told me she couldn't do it anymore and my constantly bringing up situations was stressing her out, and that she knew she wasn't being the best person for me, so it was best we broke up. Can you imagine that ? I've tried to be there for this girl, dragged her to AA, been a shoulder to lean on; told her I will be there; the only thing I wanted from her was her to respect me. I guess that was/is too hard to do and she is willing to break up something which I think even 2 months into it is very special. I will miss her, but the amount of hurt I've gone through as of late, wow,..... I feel like I'm losing my mind and though she doesnt want to accept it; alcohol is always at the center of our problems. I don't know if I should tell her mother; don't know if it's in my place. Probably not..... I am so scared for her... I don't want us to break up... I love her so much. I look at this situation , and I've had more patience with her than I've had with any other gf in my whole life and she treats it like if its nothing. I'm 26 and smitten with a woman who doesn't care that she hurts me, she loves me I do believe somewhere , cause she's held out with everyone before me and gave herself to me, and shared things with me that she shares with noone; yet she is willing to not try to fix her problems, and to choose her loser friends over someone who brings goodness into her life.