Alcohol is a disinhibitor. When someone has drunk too much, the usual boundaries that make us civilized human beings can be eroded. In a way, it gives a person “permission” to say and do things that he may want to say and do but that the civilized self won’t permit.
I’m concerned for you on two levels: First, your drinking is clearly out of control. I’m glad you’ve decided to stop. It may be more difficult than you think. There are treatment programs and therapists who specialize in helping people stay quit. You’ve already seen what alcohol can cost you. I hope you will do whatever you need to do to be in recovery.
Secondly: You seem to have unresolved issues around jealously and trust that come out when you’ve been drinking. If those issues aren’t dealt with, they will eat away at your relationship — with or without the alcohol. I suspect that something happened in a prior relationship that is now impacting this one. Do your girlfriend and yourself the much needed favor of getting to the root of this problem. It threatens to destroy a promising partnership.
Trust the wise person inside of you. The behaviors that are of concern are your system’s way of telling you that you need to take care of some personal business before you are fit to make a permanent commitment.
I wish you well.