I can relate, soma.
I used to be painfully shy and introverted - when I was in 8th grade the people I went to school with actually thought I was mute! So you should know that you're not alone.
It took until I was in my mid-20s for me to develop anything like a functional public personality (I was always okay with my family, etc.) and even then I didn't know how to do introductions and wouldn't shake hands. However, I found that I was actually able to get by without doing introductions at all. I guess I just let other people handle that, but my thing was I was just allergic to social norms and small talk or something. The result? The people I did get to know were generally original thinkers, for one thing. I still tend to clam up when I'm in larger groups of people. It's okay, they'll probably think you're intelligent and mysterious.
So just practice, like you're doing. It's like you're conditioning yourself to be less stressed in social situations. School in general is a great place to learn, so you're in the perfect place. Just practice saying "hi" to people - you don't have to have a particularly important reason. Or engage them in dialogue by either asking or offering help of some kind, like directions to a good coffeeshop or something. Another great way of breaking the ice is humor - you can even make a comment to total strangers if something funny happens nearby, and they will generally accept it and go along.
To be honest, I attribute a lot of my social skills to drinking. Without alcohol, I might have just sat in my room reading a book instead of going out and learing how to relax and talk to people. The thing is, by practicing while drinking I learned that you really can just go up to people and say stuff, and pretty soon I got to the point that I was able to do it sober. I just needed that kick-start to get myself to lower my inhibitions. Not that I'm recommending you turn into a lush, but it might help your social life, that's all.
