Would you feel shame and embarrassment if you had cancer or diabetes? Alcoholism is a disease! It's not a moral imperfection. You didn't get it from unethical behavior or a dirty syringe. What's to be ashamed of? Being an RN doesn't mean you have magic immunity.
There are more than a few MDs and Rns in the AA meetings i go to, and once in a while they'll show up in scrubs. No one gives it a second thought. An alcoholic is an alcoholic. A question, though. You've identified the disease. Now what are you doing treat it?