There are some web sites that talk about dancing for introverts. They say it actually can work, in that they can have a limited and more structured number of interactions. That's an interesting thought that dance could actually be a less stressful way to interact with others, I'll have to try thinking about it from that angle.
This certainly holds true for me. I much prefer structured interaction - random, impromptu social gatherings with no purpose are not my idea of fun.
I am a ballroom dancer (Argentine is not my thing at all), but for what it's worth, I:
- seriously enjoy private lessons, even more so when there is no one else in the studio
- genuinely like solo practice, and love the once or so a week where I go in early and have the place to myself
- heavily prefer standard as a dance, because of the structure inherent in the form (and the fact that the hold lets me get in my own little world more easily than other forms, like latin or salsa)
- make a point to say hi or wave at people when I'm at the studio, but have spread the word that when I am there, I am there to work on my dancing, so no one is offended (or at least not too badly) when I don't have long conversations
- have learned to like competitions over time, but am generally the one off by myself on the side or in the hallway, staying focussed and being antisocial
- do not particularly enjoy social dancing, and rarely go just for the fun of it (think once a year or so). I am much more comfortable having a role at the social dance - running music, being the door police, etc. - than just being there for fun. That way, I work for a bit, dance for a bit and have an easy way and reason to structure the evening
- decide when I have enough social energy to devote to a social event, and make sure to plan in quiet, alone "recovery time" afterward
Hopefully some of these strategies will help you out. I'm sure that I employ more, but these are the ones that immediately come to mind.
The dance world is full of all kinds... trust me, the introverts are out there. Some of us may have just developed stronger coping skills having been around dance longer and having discovered our strong introversion early.