Perspective makes a big difference. I didn't think I was really an alcoholic until I had several months' sobriety. I thought I'd just been a heavy drinker. Then, when I started to look back at the events that led up to me quitting, I realized that I am an alcoholic.
When you're not drunk, you have lots of time to think. As you mull over the events of the last couple of years, you'll learn a lot about yourself. You may, at some point, decide you weren't an alcoholic after all. Then again, you decide the opposite.
Labels don't matter all that much. What matters is what you learn and what you do with what you've learned.