Sorry to hear about your difficult situation. Rehabs can definitely be tricky, as many are perpetually full and sometimes only accept certain insurance.
I would agree that AA is a great way to start your sobriety. You've already realized a very important thing - none of us can do this alone!! The recovery community is very supportive, and many if not most of us have been exactly where you are. Find the right people in AA and they will help you in ways you can't imagine, and have resources that could help you even get into a rehab. You won't know if you don't go!
Another quick note - as you know (and I know all too well myself), drinking that much a day can lead to some nasty withdrawals. Be careful if you decide to stop cold turkey; you may need help to safely detox :-)