Is it possible to become physically addicted to alcohol, but not be an alcoholic?

You're much better off not drinking if you have a history of drinking to excess. I've been to hundreds of AA meetings, and I found it to be a religious cult. You don't need God to help you stop drinking. I did it by myself. AA meetings just made me want to drink more. It sounds like you're doing well, and you've found some insight into the problems that made you drink. Work those out with a therapist.