I was a sorority girl at UCLA. I think the whole rush process is pretty much the same. As for being a “plus size,” I know that sororities get a bad rap for being vain and appearance oriented, but that’s not always the case. I was a Delta Zeta; our house was in the news a few years ago for discriminating against larger girls. But I was a ‘plus size’ when I rushed, and I’m Asian AND was an astrophysics major! Three strikes! lol! But I still found a house that was the right fit for me. I doubt Aggie girls would be as mean as UCLA girls. LA is all about vanity 
Don’t worry about being shy! Just try your best to be yourself. It’s NOT a job interview. You’re finding people you want to hang out with. If you don’t get picked, that doesn’t mean you weren’t good enough for them. You just didn’t click at that moment. The houses will try to get you to meet as many people as possible without diluting the process of getting to know you as a person. Just relax and have fun 
If you want a recommendation for Delta Zeta, I can write you one