There is a phenomenon among new members that I and my best friend from college dubbed:
"MY SORORITY IS THE CURE FOR CANCER!!!!"
Women who suffer from this ailment find themselves spontaneously drawing the symbol of their sorority underneath their name every time they sign it. (This often might occur while they are writing on others' dormitory door whiteboards.) They like to talk about their sorority incessantly to everyone around them, even if those people are not particularly interested in their sorority or Greek Life generally. Indeed, sometimes a person's lack of interest will egg the new member on, as the new member tries to convince them that really, their sorority IS the cure for cancer. These women may plaster every surface of their dorm room with sorority colors and symbols and wash their bid day shirt several times a week so they can wear it more often (bonus points if the new member buys extra t-shirts from the sorority t-shirt vault in order to wear her letters more often).
This illness may infect even the most rational, stable women. It usually persists until AT LEAST the end of the new member period, and often all the way through the following years' recruitment.
So yes, your obsession is perfectly natural.

I think having one is a normal (and exciting!) part of the cycle of sorority life.