Like you, I was incredibly embarrassed by my drinking, and the thought of admitting I was an alcoholic made me want to curl up with cringe. Unlike you, before I could admit to myself that I had a problem, others around me started noticing, and that was far more humiliating than going to the GP to ask for help would have been. Even with the knowledge in hindsight, I'm still not sure if I would have been able to convince my bottle-of-vodka-a-day-drinking self to self-refer for help, that's how ashamed I was. I get it.
However, the very first addiction group meeting I went to (not AA, but similar), I fully expected to be full of street drinkers; grubby old men and homeless people. It wasn't. I was 31, a professional, married mother of 2, and I was shocked by how many other women, just like me, were in the same boat. Our drinking, which had been a treat at the end of a long day, or a way to unwind after the kids had been driving you crazy, had taken over our lives, and was costing us more than money.
I've been sober for 12 years next month, and although it was tough to begin with, the very hardest bit was admitting that I had a problem, and you've already done that @Peaky777! Your GP likely sees a couple of women in a similar situation every week, and will be able to provide all the support you will need.
These days I'm happy to admit to people that I'm an alcoholic, because being a sober alcoholic is something to be proud of, which is incredible considering the shame and embarrassment it brought me when I was drinking.