Dude, give it a shot. I've been in bad situations with relationships and as one guy to another, you can't let that stop you. I've been trying to have emotional connections for the past two years and until I met my girlfriend it was incredibly difficult. You're lucky to already have feelings for someone, and you should not let that hold you back. Ever.
Ask her out for lunch again, or to go for a coffee, or something. Go out with her. If you're shy, don't hide it. If you're nervous, tell her at some point. Don't make a big deal of it, just go out and do something fun together, like go for lunch or a movie or, heck, go mini-golfing. I dunno. Do something together that you both want to do. Show her who you are. And heck, at the end, ask her if she would like to go out again sometime.
If you got the will to go out, go out!
And in relationships, or in life, remember some important words:
"Do what you fear, and the death of fear is certain."
You got a chance with her. And you got a chance to be happy. Take it.