I never got along with the opposite sex (or even just "cool" people of the same sex ) better than when I didn't care much. I used to get so keyed up about these things, but whenever it didn't matter, I found friends in the oddest places. Easily.
I guess the only advice I have is to relax and not worry about it. In the grand scheme of things, you'll have a ton of successes and a ton of failures, and you really won't remember more than 10% of it. Seriously. Have fun, be a solid person who knows him/herself better than anyone else and try to make the connection. It will work, or it won't. You may not be at the age yet where that can feel natural, but that is genuinely the way to go.
The problem is, as she is not in my class, but the parallel one I wouldn't really see her that often if I just go with the flow.