Odd Girl Out
This is a reprint of the book.
Three other versions of the book.
This is one of the pulp novels, originally published in 1957, which were written by Ann O'Bannon. They were quite a sensation when they originally appeared, and there are several novels featuring similar characters.
Laura is the main character in this novel. She's lesbian, and has a mild case of SIV (Self-Inflicted-Violence.) She falls for a girl named Beth.
Laura is accepted into a sorority. Emily is also in the sorority. The main focus of the entire book is Laura's relationship with Beth, and how Beth, in the end, finds herself more attracted to men. It's basically the typical the-lesbian-loses type of novel of the era (and the lesbian generally had to lose, according to the standards of writing of the time.)
It's a very tame novel by today's standards. I think it was, essentially, a rather boring novel, with too little basic material being stretched too much to fill up an entire book.