Based only on what you've said:
You sound young, insecure and nervous. Perhaps do seek treatment for your anxiety, talk to someone about it, especially if it is what is holding you back from being able to work. Consider volunteering, finding things to do that you are interested in, working towards goals of some sort. Exercise outdoors. You need to find things to DO, and then see if drinking doesn't just naturally fall by the wayside. I would date somebody other than this girl, for now, but that's just me.
I didn't see certain key phrases in your post, things like once I start I can't stop, I say I'm not going to drink again but I always do, I feel ashamed, I notice I drink way more than everyone else, I always drink to the point of being very drunk, I never just have one or two... Things like that point to alcoholism.
I think that people who use alcohol as a social lubricant run a higher risk of being alcoholics in the future, if they don't find their place in the world by any other means. If it comes to a point where "the only time I feel good and like myself is when I drink" then it's a problem.
But remember that it's never really a healthy thing to do, even in moderation, really. It's not something you have to do. If you begin to feel uncomfortable with your amount of drinking, start by cutting back and see how comfortable you are with it. If it gets to where you are extremely nervous in all situations and the urge to drink is at the forefront of your mind, that's a red flag that you could be starting to have a problem.
A trial seperation period is a good idea.