Hello Leshar,
I know this is difficult. I am also a very visible professional person, and many people know me. In my profession I have a rock solid reputation, and some people at meetings who know me are visibly surprised, but that wears off in minutes. We all go, regardless of the mask on the outside, because we are alcoholics, and we want to improve our lives. Were these closed meetings or open to the public?
My first reaction was that even though these are peers, and former patients, they are alcoholics too. We establish a brotherhood in our AA groups, with a high regard for the anonymity part of it. I don't think you were betrayed at all since it was two people in the group having the discussion. We look out for each other, and there may have been a lot of concern in their conversation. You are new, do you have a sponsor? That will be very important, and a good discussion to have with them.
I would advise you to keep your eye on the prize. Lifelong sobriety is worth almost any price, and it also means that if you are giving AA a try, that you embrace and work the 12 steps. Step 1 says:
We admitted we were powerless over alcohol—that our lives had become unmanageable.
Concentrate on that "unmanageable" part. You are giving up the control of all situations in the first 3 steps which are the foundation of the entire program. I wish you the best, you cannot do it alone, and AA works for many people. I attend meetings regularly and the experience and insight are priceless if you truly want to stay sober. I learned long ago that I had to check my ego at the door when I go to a meeting, it has no place amongst the comrades you will find there. Hope that helps.