Hmmm. It sounds as though there may be some underlying problems in your relationship. You say you want to spend the rest of your life with her but you both don't like each other after you've both been drinking. I wonder why? Not that you have to like everything about each other (that would be dull) but what other things lie beneath the surface. You don't say how long you've been together but it sounds like it's been awhile.
It might be a good thing that she wants time away--you ought to take advantage of it. This time away could be longer than a few weeks and putting your life on hold hoping for a good break to come your way might be impossible. The time away will help you sort out the issues that you appear to have. What are you looking for in a relationship? What do you have to give? How much are you willing to compromise?
The idea about talking to a mutual friend is a good one but she may not tell the friend the real reason because she may not know herself. It's obvious that something is wrong but the real reason may be more than meets the eye. Not that you're both deeply disturbed, I don't mean that!
What kind of a support network do you have? Friends are of major importance right now. Call in your chits and lean on them. Forget any mutual friends, however. You need to take steps on your own way towards feeling better about yourself. If you don't like yourself you won't like anyone else.
Time to take up a hobby or an interest you've wanted to do. You'll meet other people that you can share an interest or two with. This will also help you to become a more interesting person to your girlfriend and/or any subsequent Significant Others.
I know it sounds so easy to do this but I'm 51 and have gone through my share of heartbreaks and have given you what has helped for me. The most important thing is to take the first (and hardest) step. Yes, you'll have bad days but they'll be fewer and fewer as you get better.
Good luck and do keep posting.