Why would want to continue a "friendship" like this? It sounds like a very uncomfortable situation, not a friendship. Maybe she needs some help, but you aren't a therapist. Friends are people that you enjoy being with and have much in common, feel free to be yourself around. Friends aren't people you only feel sorry for.

You might try some of the very good suggestions made by other people here, especially Peppermint Patty. But if that does not get her going and coming out of her shell, then the best you can do, if you feel comfortable enough, is tell her as kindly and constructively as possible how you feel. Suggest she may want to see a therapist to help her explore her feelings more, to be able to open up to other people.

If you don't feel comfortable doing that, then I would just let the relationship go, don't be rude. Just be "busy" when she calls, try to find other people to sit with or talk to at school, or say you just feel like being alone, you have a lot of work to do.

If this happens to her enough she may start to question if she has a problem and seek help for herself. Or she'll simply find other people who only want to talk about school and church and they'll all be very happy and interested in that together. It does not sound like you are.