Lauren,
Do
NOT let being shy stop you from going through formal Rush!!!!!!!!! I was extremely shy when I went through my own formal Rush, and some of the parties were a little awkward because I wasn't sure what to say or what questions to ask. However, I found out very quickly that I felt comfortable with the DZ girls in their parties and that I had a far less difficult time carrying on a conversation with them than I did the other groups on campus. You'll probably feel that way with certain houses also and that's how you know that you "fit" in with those particular girls.
My suggestion is to make a list of questions going into Rush that you can be prepared to ask if there is a lull in the conversation. Most of the time, you're only going to be speaking with one or two girls at a time, so it's not like you'll be bombarded with a group of sisters all at once. And, most of the time, they'll be asking you simple things -- about your activities in high school, what your major is, why you're rushing -- things like that. So, relax and enjoy yourself. The sororities are trying to impress you just as much as you're trying to impress them. And they are used to dealing with shy rushees - trust me!
I think that the biggest positive thing that came out of my collegiate years in Delta Zeta is that I am no longer a shy person. I can pretty much carry on a conversation with anyone now, and I attribute that skill to being in a sorority. You can't help but learn to open up when you have so many sisters to meet!
Good luck! Please let me know if you have any questions. And definitely take IowaHawkeye up on her offer of help. She knows the ins and outs of Rush at your soon-to-be school and can answer most of your general questions.