Can I be frustrated at a 14 year old girl who constantly talks about her personal problems?
What's wrong with the 14 year old? She is still young.
She talks so softly and so sadly, I feel like the only way to deal with her is either to become her friend or to vent on her to release my anger.
I get your point, but you should refer her to a therapist if she's having problems. And it's normal for teenagers to talk to adults about their issues.
She's such a crier, I'm frustrated
Unless the problems are serious, you should get her professional help. If it's not, then see if you can get her parents involved. I know you are a patient and kind person to hear her out, but don't get angry because teenagers are usually quite emotional about silly things.