Unless you have another, more pressing (hard to imagine), medical issue... Make it the very first thing you say after your hello. Get it out before you have had time to think about it. This is also important because the doctor isn't going to have as much time to spend with you if you finally get the courage to bring it up at the end of the visit.
Also, if you are more comfortable with the nurse or medical assistant who brings you back to the exam room, just mention that you want to talk to the doctor about something very important... you can either tell him or her that it's about your drinking, or that you are embarrassed and that you will tell the doctor directly.
They are on your side!!