What should I do in a situation like this?

Saveable? It's not in danger! It all sounds great. Not everyone jumps straight into making out and lovey-dovey straight away. It sounds like she is a nice girl and she likes you. If she would like to go further she will help it happen, believe me. Go to the party. Think of a nice date. Observe to see if she smiles at you a lot (this is a good sign). You could even ask her if you could kiss her.

Thanks for the great advice! Yesterday she almost choked because she laughed so hard, so yea she laughs alot when she is with me.

Maybe I am just overthinking everything (I do this alot).

I agree with centrox (hi!) - it sounds lovely.

I recall a guy asking me (oh my God, you don't want to know how long ago this was) if he could hold my hand. I found that utterly charming.

Have fun and don't overthink it. You're doing great. Name the kids after us!

The next time you guys go out or hang out, sit NEXT to her, like plop down right next to her. Close enough so that while you guys talk and laugh you can make some physical contact. Bump shoulders with her to emphasize a joke or comment, touch her arm, grab her hand with an "Oh my gosh did you hear about". These are pretty innocent ways to break the touch barrier as you call it. She will reciprocate if she likes it, if she doesn't...ehhhh...could mean a lot of things. Assuming she doesn't run away from you, it should be more and more comfortable to initiate and have physical contact like holding hands, hugs, arm around the shoulder, and the eventual first kiss and whatnot.

I applaud you for taking your time

As an aside, physical contact is just another way to connect with people. It doesn't have to be sexual or whatever. It deepens the relationship. My best friend is female and we have always hugged as a greeting and as a see you next time. I wouldn't dream of any sort of romantic relationship with her, it's just what we do because we are very good, long time friends.

I once asked a girl if I could kiss her and she said "Yes, please". This was before the Apollo moon landings.

Dave, is that you?

Hi, honey!