I'm sorry you're going through this. I've experienced it too and when I learned to enjoy myself a little the loneliness doesn't seem so bad.

If this girl doesn't seem to like being around you then let her be. She'll call or visit you if the friendship means anything to her. I recognize what you're explaining. I had a friend like this once too. It wasn't long before I started feeling that our friendship was a pity case for her. Our conversations revolved around her and her events. She wasn't any good at showing any sort of concern for others.

You should keep looking for more friends to spend time with. Maybe try other means of meeting people?