I agree with a lot of what's been said above. You probablly feel like you are unusual because you're shy. The fact of the matter is that most people feel a little shy in these situations. Unless you experience flop-sweat in this sort of situation, I wouldn't get overly concerned.
It is important for you to understand that recruitment is really a MUTUAL selection process. You will be feeling awkward and so will many of the GLO members. After your first round of events, this will likely subside a lot. However, you need to demonstrate your interest in each group by asking questions AND you want to find the group that really is a good fit for you. You will need to make decisions along the way of which chapter's invitations you will accept and which you will regret. The chapters need to impress YOU!
I would develop a list of things you want to know about each group. Memorize the list and fall back to it when there is a lull in conversation. Ask a question that relates to something you really want to know. AND it is REALLY ok to ask the same question of more than one member. You may feel like "I've already asked someone that question, so I better not ask it again." Not true! Ask away! The GLO members will appreciate your inquiries and you might find that you get different answers.
Here are some areas I would want to know about if I was rushing all over again ...
What's it like to be a new member? What are the requirements? When are the meetings? What do I need to do in order to be initiated?
If the group has a chapter house ... What does it cost to live in the chapter house? Is it a requirement for me to live in? Who gets to live in?
What kind of community service do you do? Do you just raise money or do you actually get out in the community and help people?
What kind of academic support will I get from the sorority? What kinds of academic standards do you have? What do you do to keep members motivated? Are there scholarships available through the sorority? Has anyone in your chapter ever got one?
What kind of other campus organizations are your members involved in? Do you have any campus leaders in your chapter?
Etc ...
Maybe others have some ideas too, but this is how I would handle it.
Good luck, my dear! You'll do great! DON'T WORRY!