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A couple of things came to mind when I read this post...
First, you say that you haven't been invited out by anyone. Have you tried inviting them to anything? Given the situation with your big, everyone may just assume that you have other friends or things going on, since you didn't interact with them before, and not think to invite you. If you were to invite them to do things with you, it might encourage them to start inviting you as well. Could you and your little invite them to something together, if you're not comfortable inviting them on your own? Also, it wasn't clear from your post if your chapter has a house--if so, have you been spending time in common areas, or just sitting in your room alone? I'm an introvert, but as a student, I found that I met more people and had a better social experience when I spent more time in common areas.
Second, I wanted to encourage you to consider counseling to help you to feel less awkward and more comfortable socially. That's the kind of thing that college and university counseling centers are there for! You can choose to leave your sorority, if you truly feel that it's a poor fit for you, but the feelings of loneliness aren't likely to go away unless you can find ways to reach out to others. Talking to a counselor on campus might help you to feel better and come up with ways to reach out to people and make new friends that have something in common with you, whether it's through your sorority, in class, or through other organizations.
Good luck with whatever you decide.
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