Apparently I was really offensive at a party one night. What to do?

Ok so a couple of weeks ago my bro had a big keg party with over 50 people. Now to start this off I will point out I'm not very good at picking up girls plus get anxiety and drink too much in big groups and when I'm drunk I think I can pick up anyone. So apparently I started off the night after beer 9 dancing with my shirt off and made some really offensive comments to this one girl who happened to be married to my sister in laws cousin's wife. I basically said straight up that I thought she was hot and hit on her a bit too much and it didn't work out. Of course I heard about this the next day completely hungover and suffering from amnesia. Then my bro was making stuff up just to mess with me so I don't know if I believe it or not and my sister in law says nothing happened. So I don't know who to believe! What if I run into the girl again? I'm a douche when I'm drunk and tend to get Rob Ford drunk after a few beers, but when sober I'm usually a good guy. Any advice here?

No need to apologize because face it if you were really that offensive her husband would have
knocked you out at the party. There's nothing to say I'm sure she doesn't even remember the
incident. The problem with people is they think they affect others long term, most don't even remember
parties the next day.

Lightly apologize to all you may have offended and… Drink less from here on out!

But… However you are basically covered by everyone else's bad behavior under the influence so… Lightly apologize and go on with life.