This easily could have been written by one of my own lils. I'll be the first to admit that I wouldn't have won big sis of the year. However, my own big was even worse. So it's not like I had a good example of the way a big should be. If it weren't for the fact that you said she's close w/ the other lils I'd suggest maybe she has a similar problem.
You're right that it is her job to make you feel welcome. But we don't know why she's not calling you. I rarely called one of my lils because she had like a million different activities. I could never get a hold of her so I gave up. So maybe you can call her once in a while. She could be thinking that you were disapointed w/ her. Attempt to call her once a week. I bet she'll respond very quickly.
Here are some suggestions:
Her other lils are your twins. Call them!!! You must have something in common w/ them or you wouldn't have wound up w/ the same big.
Screw your big and ask another sister to adopt you! I would give her another chance before you do this though. Her feelings will definitely be hurt. But you need someone that will be there for you!
Bond w/ your pledge class and mom more. They'll probably be w/ you longer than your big.
Your big is only one sister. There's an entire chapter that should be making you feel welcome. Don't be afraid to confide in them.
Vow to be a better big than she was to you!