I wouldn't worry too much about the insurance thing. If it really bothers you, suck it up and pay for the first office visit and talk to the doctor about your concens. An office visit usually isn't more than $100-$150, you should be able to pay that back in alcohol savings in a few weeks. Honestly, I really wouldn't worry about it though. It's not like the insurance company is going to share that information with anyone you know anyway. Ask the doctor just exactly what they have to be told, to ease you fears. You may be able to find that out over the phone when you make an appointment.
Does your family have any idea what is going on? Even if you don't think they do, they probably do. Hopefully they will be supportive. You probably will be a bit of a pain to be around for awhile, but honestly, you've probably been a pain, or at least a worry with your drinking. Try not to beat yourself up too much. I say this, but I am probably one of the worst at doing it!! I'm working on it!! Congrats on making it through the day. Take care,