I have never gone through this and I am not an alcoholic, but I hear you.
One thing that really stood out to me are the 3 sides to you. You know, there really aren't 3, all of them are you. You are exhausted because you are fighting yourself, that must be quite a fight! The fight isn't over until the ONE you is exhausted, that's the only way it can end.
To me, accepting yourself, as you are, is the first step to loving yourself. I think sometimes people imagine, how can you love yourself if you don't like certain things about yourself, well, by acceptance. The good and the things you may not like. That doesn't mean there aren't things all of us can work on, just means we are human.
None of the things you have described are weird or odd! All of us get conflicting feelings sometimes, even about good things.
Dating is about getting to know someone, all the good feelings are flowing, I think it's a really good idea to take it slowly and just see how it goes, try not to hop too much in to the what ifs and looking way down the road, just enjoy your time together and see where it goes. She obviously likes being around you!
Above all, just be yourself. She deserves that (and so do you).