I'm not sure as I understand why you feel so stupid. You reached out for help...you'll be going to see a counselor and hopefully, like myself, get yourself in some kind of rehab. It all takes time. There is no magic pill. The foremost thing you could do right now is not drink. Congratulations on going to see the doc. Great progress.
BUT if you think you are having more serious medical issues and need your blood drawn then make another appointment for that in particular. Maybe you didn't tell her what you expected from the visit.
I found that patience was a huge factor in my recovery. I needed to learn how to slow down, take a deep breath and except things for the way they are -not the way I expected them to be. I think you'll be ok...as long as you don't drink.