Am I really an alcoholic, or am I something much worse?

You probably have PTSD and you are using the alcohol as medication. I think you should go for counseling to help you get back on balance. My brother-in-law has the same problem. He was in the Army and has PTSD. He used the booze to deal with everything too. He is seeing someone with his VA benefits and was able to quit the booze. I think you should check into that. I think that AA won't do you any good at all, since it's much different and deeper than just an addiction. (PTSD is Post Traumatic Stress Disorder.)