Good news...
1) Ten+ years ago.
2) One-time event.
3) BAC barely at the legal limit.
Odds are that the AME will be able to issue you a 1C on the spot, although the FAA might possibly follow up with some additional requests for information.
I would talk to an aviation medicine consulting company BEFORE you talk to the FAA or an AME, just to get all of your ducks in a row. You will want to have all the paperwork, including case disposition and most especially BAC.
As for airlines.... regionals won't care (some actually prefer DUI's because they know you'll stick around longer). For majors it will delay your call but by the time you get there the impact should be minimal for the reasons I mentioned. But you need to keep a clean record in all things because you already have one strike...