Pennylane,
The definition I like best is given by AA's Big Book, page 44, as
Originally Posted by AA Big Book, 1st Ed.
We hope we have made clear the distinction between the alcoholic and the non-alcoholic. If, when you honestly want to, you find you cannot quit entirely, or if when drinking, you have little control over the amount you take, you are probably alcoholic. If that be the case, you may be suffering from an illness which only a spiritual experience will conquer.
Are you able to quit entirely? You're coming up on a month and having some creeping thoughts. Can you do that for a year? Do you have control of how much you drink when you do drink? Do you experience the phenomenon of craving when you drink? That is, is your body and mental reaction to want to drink more once you start.
I think, from a recovery standpoint, it's very important to understand if you are an alcoholic or not. Consider these questions carefully. It's easy to be dishonest with ourselves.