AA can be really hit or miss (my sister is a recovering alcoholic) - some groups are better than others. And it can take a while of sticking to it to stick to it. So you may want to see if you can find another group until you find one you are comfortable with. If you can't if you can find yourself a sponsor - another recovering alcholic that you can just call who will understand - that can be the biggest help in the early days (and later, too). Its both the support of someone who understands, and being accountable to someone who is not invested the same way your family is.
In patient or outpatient treatment is often helpful - and usually covered by insurance.
I'd start by making an appointment with your family doctor and getting a therapist that specializes in chemical abuse - like AA groups, therapists have a lot of variaiton, try and find one that works for you. If you belong to a church, your minister might be a source of comfort - and may be able to help you with resources. Our church provides pastoral care, and we've done pastoral care for alcholics who don't want to do AA by setting them up with a sponsor outside of AA.
While the AA group you went to was not helpful, one of the things all the people in recovery I talked to - fans of AA or not - repeated was the "one day at a time" mantra from AA. For right now, I will not drink....for this minute. For this hour, I will not drink. For today I will not drink. As you string along the minutes into hours, the hours into days, you'll find you've been sober for years.
Good luck and may you find peace and strength.