Will your insurance cover 90 days? THere is a great progam in VA.
The danger of rehab (as opposed to detox) is that you will get separated from your desperation to get sober. A detox should be able to taper you off alcohol and benzos safely within a few days. After that, you can go to AA if you are willing to take certain steps to get sober and if you sincerely want to get sober (and if you are a true alcoholic). NA can help with the drugs part. There is a difference in the first half of the first step that relates to the nature of powerlessness around drugs v. the nature of powerlessness around alcohol.
Congratulations on this big first step toward a new and amazing life. I was where you are now 6 years ago and there is such an amazing life on the other side of addiction to drugs and alcohol!