1) Toastmasters. This is like alcoholics anonymous for people that are addicted to shyness. And very likely there will be some people there that are even more quiet and introverted than you are.
2) Social dancing. I'm guessing you are male, in which case you will be in high demand. Even if you are overweight & ugly as sin, if you can keep a beat then the girls are gonna want some. If you are as intelligent as you sound then this is also a big plus: the smart people end up being the best dancers. And it's not about talking or being interesting, it's about the mechanics of space and time (physics and music). I would recommend tango: this is where all the real nerds end up.
Getting over the fear is not going to happen on its own. Instead I would suggest finding something where you are more excited than afraid.