I am on about 3 weeks as well. Tonight I went to my first sporting event, booze-free. I was invited by an old friend and her co-workers. I almost turned down the invitation because I knew that everyone would be drinking, there would be plenty of beer and offers to get "free" drinks on the company's dime, but I hadn't been out socially in nearly a month, so I went for it. Before I went, I planned on buying my favorite ballpark treat, and splurging on pre-game sushi at the bar near the park. I sipped diet coke and iced tea. When offered a drink I simply said that wasn't drinking tonight, because I was getting over a cold. To my great surprise, everyone was totally chill about it, and I had just as much fun as games where I have been drinking. In fact, as a bonus, I remember every moment of the game, didn't have to miss as much for beer runs and spent far less money than I normally would.
I know it isn't exactly the same, but I would say 1) plan to treat yourself (maybe have an extra piece of wedding cake or get yourself a new outfit) 2) figure out some tasty non-alcoholic beverages (cherry cokes, etc are free too!) 3) Have a line ready in case anyone asks ("I'm getting over a cold, on meds, etc") and 4) Maybe volunteer to be a DD for friends/family (it might help to know that your abstinence is benefiting others)
I'm pretty private too, and although I have spoken to very close friends and family, there is no reason that you need to tell everyone or bring up your addicition issues at a wedding. Good luck and have fun!!!!