Personally I've never described myself to others as an alcoholic, when I'm with people it's simply "I'm not drinking today"!! It keeps life hassle free, however in private in my own head I know the reality.
Also I tend not to focus on the definition of an alcoholic, because as you did in your post you rationaled the problem away, "well if I don't drink in the morning and can go a week without maybe there's no problem", I was the same, never missed a day at work, never drank in the morning, never lost my license.
But you and I both know drinking leads to big problems in our lives, and so whatever we choose to call it, something still needed to change.