you don't have to say "I'm an alcoholic." Period.
I had a sponsee who even after two years in AA never said it once at a table. He'd just say his name and his last drink date. My instruction to him was to be honest and if he wasn't sure or didn't think he was an alcoholic it was best for him to be honest and NOT lie by saying he was one.
"The only requirement for AA membership is a desire to stop drinking." Anyone with a desire to stop (or stay stopped) drinking is welcome.
All that being said, it may help you to find out what definition AA uses for alcoholic and what does and does not constitute alcoholism. You're certainly welcome to your own definition but it helped me to learn what AA considered alcoholic when it came time for me to introduce myself as alcoholic, addict, cross-addicted, or whatever at meetings.