Something just like that happened to me once, where I met someone (it was here on WP actually) and was having a great time talking to him, and we both discovered we liked each other after which point I became very nervous and scared that I would screw something up (I could barely eat for about a week after finding out). I decided to come right out and tell him about how nervous I was, and it turns out he felt the same way. Maybe if you were up front with her about your feelings? Another thing that I found has worked extremely well for us is that we decided to be as open and honest with each other about things as we could, right from the start-one way this has helped us in that we have always been clear in terms of where the relationship is going, so we didn't worry as much about moving too fast, or too slow, or anything like that. Also, remember that you've been yourself with her so far and that she likes you for that, so there's no pressure on you to be any different
If you are anything like me there will continue to be times that you feel nervous and afraid of screwing things up-I still get that way even though he and I are now engaged-but sometimes you just have to go with it, as scary as that can be, and be honest and be yourself and trust that everything's gonna work out. Also, I know a mistake I've made when I got scared was trying to push him away from me, but luckily he was very understanding about it. This has the potential to really hurt someone though, so if you find yourself on the verge of doing this, be open with the person about your fears instead. Sorry if I used too many cliches there
Good luck with everything, I really hope it works out for you.