I'm surprised the doctor didn't order blood work to test liver function, cholesterol levels, and triglyceride levels among other things. When I first told my Doctor I had a drinking problem she ordered the blood work and generally doesn't let me go too long before having it done again.
But, she did tell me that as a Doctor she wasn't trained in counseling or conditions involving mental health. So, she recommended I get treatment for that.
One thing that is common for people who have been drinking for a while is high triglyceride levels which is something you will want to know about. The Doctor can provide medication for something like that to keep it at normal levels. So, I would try to find a doctor that will send you to the hospital to get the blood work done. I think it is a normal procedure and insurance should cover it. But, that is only my guess.