How do you get to know people after being a b. i.t.c.h.?

ok not really a "*****" but I have social anxiety and i think my super shyness comes off that way to those that don't know me. I'm in a sorority (yes, shocking) but i like it (at least what it has to offer) what gets on my nerves are the girls. sometimes they can be sweet, but most times they act like i've treated them horribly! in the beginning i was overwhelmed and was just learning thro therapy how to have better social skills, so i was not confident and they probably took it as i don't like them. now they act like a holes when i try to get to know them. i reach out to them and ask to hang out/get dinner and get ignored or i get a yes, but no follow through. it's all fake (i HATE FAKE). i figure they are defensive b/c how i came off before, but then their rejection of me makes me act like a ***** in return only furthering their umptions of me, and the cycle starts over. i'm actually a very nice, compionate person with super close friends and family who say i'm fun, sweet, and true to my values. i just want to sorority girls to see THAT! It makes me not want to hang out at any of the events, and then I'm that bad guy b/c i don't come to anything. but who wants to go somewhere they don't feel welcomed? How can I show them I'm not a *****?