Good for you for making a Dr appt. I hope you followed through with it and were completely honest with the physician. You will not be the first patient he/she has seen with an alcohol issue. Although you probably feel alone and as if you are the only one who has felt the way you do, it is all too common unfortunately. I have been sober now for over 2 decades and understand the compulsion despite one's common sense telling you otherwise.
It is not an issue of bad character or poor morals. It is a medical condition. If you attend an AA meeting you will find that you are not alone, I would also recommend that you acknowledge your own worth by giving yourself permission to take the time to enter treatment in an abstinence based program. I did and it changed not only my life but the lives of my loved ones and friends. It basically gives you a whole new perspective on life and how you live it.
I remember well thinking that I was hiding my drinking "problem" from most but discovered when I sobered up that EVERYONE knew. Few judged me but rather were happy and proud of me for getting help with overcoming. The ones who matter were all very supportive.
Sounds like other than who may know of your drinking you do not seem to be in denial about having the problem...that is always the hardest part of recovery and the first step in AA " I am powerless over alcohol". It's been a couple of weeks since you posted, I hope that you have reached out and are on your way to a better existence without alcohol. My worst day sober is far happier than my best day drinking.