Welcome to SR Jessica. Congratulations on getting through those cravings and well done for going to AA - that's something that most people find very hard to do, so that's excellent - you should be proud of yourself!
Only you know whether you are an alcoholic or not, but coming here and going to AA suggests that you know that you at least have an issue with alcohol and want to overcome it. I don't think it matters or not whether you are technically an alcoholic, the fact that you are working on sobriety is excellent and I applaud you.