I think those casual gatherings are exhausting because of the introversion, not the other way around.
There is a quote by someone (African woman and we already talked about my memory!) that is along the lines of "blah blah, it's your second thought that shows the kind of person you are." We all do stupid things if we're not paying attention, but if you think twice, change your reaction, you're probably not going to hell.
Maybe? Things that don't bother me are formal gatherings with my peers or gathering with my non-peers. That is, I can speak in front of a group of engineers at NASA no problem, whether they are at my level, below me, or above me. Not shy at my wife's church, or at a ballroom dance, or at a meeting of the local gave rescue group that I'm apart of. Plop me down and ask me to entertain kids, no problem.
Take me to a party, surrounded by my friends, and I'm ready to leave before I get there.
The second thing you said - it seems like for every profound saying there is an opposite profound saying. I would wager the one I'm looking for would describe the first thing you do as describing the 'real you' - the thing you do without thinking and second-guessing yourself. in vino veritas or some such. It's nice to think (and probably true!) that in my contrition, I am somewhat redeemed, but I would prefer to be the person who never had to feel contrite, because I had not wronged anyone.