Munchkin,
I am retired Military. I made the mistake of not admitting that as in my last 5 years or so I became an alcoholic. It is not great to have in your records while active duty, but is a big hole in your records when you retire if that is your plan. I also taught some of the AF program. I am long ago retired but don't you realize that if that means separation they will rehab you first. Get sober with them now and get the alcohol problem in your records. Then do the rehab program and succeed for life in it by getting sober. What do you have to lose? The addiction? I think you may find that if you want to get better, you will very soon. If given a choice make sure you volunteer for any in patient or in army programs offered. They cost a lot more on the outside. However I used the VA for in hospital detox and rehab and I am not a homeless wreck by any stretch. Stop being afraid if you can and start looking forward to the relief of no longer hiding and fearing.
Good for you!