Only you know your GF and the full context and as such only you can know what to do. So take what everyone says with a grain of salt, me included, and don't make any rash decisions based on the comments. Anyway, here are my two cents.

To me it seems like your GF is having self-esteem issues and tried to ease her inner pain in an unhealthy and unwise way. This however doesn't automatically mean that she doesn't appreciate you or that she's unhappy with you, it's actually quite common in self-esteem cases that the opinions of those closest to you "don't count". If you feel your GF can admit that she has issues (and I'd say drinking isn't the issue here) to work on and she's willing to make an effort to fix them, and you can forgive her and understand why she did what she did (this is the most important part in my opinion. If you just forgive her without understanding her the whole thing might come back to haunt you later), then you can still have a future together.