It's worth talking about a few words you won't see much of here - and why I think it's entirely up to you what you call yourself, or what you call your problem.
I don't tend to use the words 'Alcoholic', or 'Alcoholism'.
Firstly, calling someone an alcoholic has always seemed to me to imply that everyone with a drinking problem is the same. It's also used very loosely in general conversation and in the media, and usually in a very negative and judgemental way.
Surely it's more helpful to treat each person on their merits, and to work out why they might have developed a drink problem, and how they might be able to resolve it?
Secondly, if you think of 'alcoholism' as a disease, you might start thinking that it's not up to you whether you drink or not. “I'm helpless. What am I to do but to carry on drinking? I'm an alcoholic!”
I'd rather think that drinking is a choice - a bad choice made in the midst of a sometimes overwhelming compulsion.
The good news about looking at it like this is that you can take your life in your own hands and change things for the better.
That's why I wouldn't be so impertinent as to call you an alcoholic. However, if it helps you to make sense of things by calling yourself one, that's absolutely fine - you're in charge.