a nervous wreck

I know this sounds a lot like a puppy love story but it is. Even though I past my teens age three years ago. I met her in my chemistry lab at the beginning of this semester. her station is behind mine and we sit back to back most of the time. Before I see her walk into the class room, I always think I know how to breath. I really want to jump to the end and ask you guy what I should do? But the story goes like this.
When we first talk our conversation is very casual, and so are the next. The only problem is I am such a neurotic mess that I act very awkward around her. It's ridiculous to the point where I can't talk to her for more than 5 mins. I am so shy and it suck all the romance away. there is actually one time she tries to talk to me by asking how to do one of the lab but I blew it up. I was too shy.
First time we met I can see she has some feeling for me as well, and I know because it's something you just know. My friend who is a girl in lab tell me she likes me as well and it feels like heaven when she tells me that. So the problem is only me. I make the situation so awkward that she doesn't want to talk to me anymore and it's so obvious that everyone knows I like her. So does he.
So now I end up in the situation where the girl doesn't want to talk to me because she knows it will not lead anywhere, and that affectionate smile or the "how are you" at the beginning of the class is gone.
I can only think of one direct solution. I should man up and go straight to her and ask her out for a drink. you know when it is appropriate. Other than that I can't do anything else. I don't think I am searching for the answer but I am just trying to say these thoughts out loud to have more courage because the semester is almost over. I can die to see the golden flow in her hair.

Well if she likes you and you like her, you guys are set!

Instead of her going up to talk to you all the time and you doing nothing and rejecting her. Why don't you go up to her and say something to her?

Just go up to her and say "Hey [girl's name], what are you doing after class? Do you wanna get something to eat?" She will say yes and you take it from there.

Try not to sound too stiff and be natural with it. You can change the words around to whatever fits you but you get what I'm trying to say?

yea, that's what ALL my friends are trying to say. Thank you, I will try my best.

Yes, I agree, go up to her for a change and ask her how she's doing, maybe ask her about the lab or whatever. You could also go with something less intimidating - ask her if she wants coffee after class, or if she wants to study together for the exam, whatever. That tends to work pretty well. :)