First off "Alcoholic" is not a medical term, the DSM refers to substance abuse disorders. From what you've described you would meet the criteria for substance abuse, subtype binge drinking.

But since you've stopped drinking and say you have no intention of drinking again, then you have nothing to worry about. You stopped for whatever reason and were obviously not far enough along the addiction spectrum to need help doing so, so congratulations. I wouldn't worry about labeling yourself unless you find it helpful.

Addictive personality is also not an official diagnosis, the question is have you replaced the alcohol with some other activity or substance that you use / do in an unhealthy way to get the same effects as alcohol. If the answer is yes, then you may have become cross addicted, which is really easy and common.

I'd ask your therapist why it is so important for them to label you in this way.

splitimage