I think what Christina is trying to say is that, if her college doesn't approve of sororities, she could start something that is essentially a sorority but call it a "social club". There are private, religious-affiliated colleges (Harding University in Searcy, AR comes to mind) that have "social clubs"--essentially fraternities and sororities, greek names and all, but under a different name. I guess because, unfortunately, the words "fraternity" and "sorority" have bad connotations to some people that "social clubs" are just more acceptable. I dunno. I have a friend that goes to Harding and is in a "social club" there called Kappa Gamma Epsilon (I think).
CHristina, if you think your college would not approve of a sorority, then it might not be a bad idea to call it a "social club" but essentially be a sorority. Let us know what happens.