A healthy friendship is driven by compromise and understanding - they tend to break apart if it's centered all around one person. It really isn't fair for her to expect that you understand what's going on in her life if she's not telling you and it's not fair that she points out your faults, but gets upset when you point out hers.
I think she needs to understand that you cannot listen to her problems if she doesn't tell you them.
I don't know her, and I don't like judging people, but from reading this, she doesn't seem like a very good friend. If I were in your position I'd have a talk with her and tell her how I feel, and asking her how she felt. No arguing.