I don't think popularity is really a factor of it, nor should my personality be used against me in an argument. To suggest that the formal is for popular/outgoing people is also a bit ridiculous; most schools have an overwhelming majority of their students attending their formal/ball. I know you are trying to emphasize with such types of personality, but is the habit of feeling sick at the thought of being around people something which anyone, especially a school, is trying to endorse?
Your argument about money is perhaps understandable (as somewhat addressed in my post), but I am pretty sure that the formal is made compulsory to both make the event as fun as possible for everyone, and also somewhere in the back of someone's mind, it is to encourage appropriate social behavior.
If you are actually in some financial hardship, just to weigh it up; a Limo will cost 30 dollars (if you want one), your ticket(s) are probably 90(180) dollars, a corsage is 20 (if you want one); and as I said before a suit is an investment, so if you can spare it, I think it is worth it. That said, your mates will (should) understand completely if you just come on your own (having a date doesn't matter much).