"I drank too much, I hid how much I drank and lied about it. I felt bad in the morning and said 'no more' but that night I wouldn't be able to stop having a glass of wine, because you know - I'd earned it, life is hard, blah blah. And then I couldn't stop the second glass or more.
I could say "I have a an unhealthy, disfunctional and uncontrolled relationship with alcohol which made me unhappy and was harming my life" but really - how different is that to an alcoholic?"
Yes, I'm exactly with Msgee. Your description is spot on for me (and I spotted you describing yourself as alcoholic 
- good for you).
I tend not to describe myself as alcoholic when talking to other people, because so many people would be confused by that - partly because they have the concept that an alcoholic drinks gut-rot booze from the moment they get up, and partly because I have been terribly good at hiding it.
But I have no doubt in my mind that I share the same mental illness that a down-and-out, 18 hour-a-day boozer does. I hope that I will be able to arrest the consequences of my disease by recognising it at an earlier stage.
I compare this with my dm who is a diabetic. My mother knows this and knows how she has to live as a consequence. She can control the impact of her diabetes by not eating sugar, by eating regularly, by keeping her weight down, by taking exercise and keeping a look out for signs of deterioration. By doing that, she has not needed insulin injections, she has not significantly reduced the blood flow to her extremeties and had to have a leg amputated, she has not suffered from blindness, and she is still alive. This is in direct comparison with her sister who was diagnosed with diabetes at the same time. They were both diabetic, the way in which each chose to live affected the way that disease played out in their respective lives (and death).