According to our national health service, in New Zealand, only about 1 % of alcoholics require medical detox, so they only allocate a few beds for that purpose. It can take anything upto about 5 days for the alcohol to clear your system, and after 5 days, the worst of any withdrawal should be past.
It never hurts to have a friend standing by to call for medical assistance if required.
From your post I was wondering if you were self medicating your anxiety. Which came first, the anxiety or the drink problem. Once you have the booze out of your system, it may help to have that anxiety looked at by the professionals.
Just bear in mind that anxiety is also part of alcholism, and if it is alcoholism you are suffering from, treating that will also help the anxiety. You will need to be very honest with yourself about this, or you risk getting hooked into a whole new addiction.