For me the moment of realization that I had a problem, was when I started having physical withdrawal symptoms if I didn't drink - sweats, shaking. Wish I could say I'd stopped when I first really realized it, but didn't and drank for a few more years.
To me, it's not important that I label myself an alcoholic. I think of myself as someone living in recovery.
Alcoholic/Addict isn't even used as a medical term anymore, it's Subustance Use Disorder with a sliding scale from moderate to severe.
I think the real question to ask, is alcohol or any other substance causing problems in my life, or is it something I want to change. When you ask and answer that question you can assess what if any help you need in reaching your goals.
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"I danced in the morning when the world was begun. I danced in the moon and the stars and the sun". From my favourite hymn.
"If you see the wonder in a fairy tale, you can take the future even if you fail." Abba