Black streaks in Phlegm, should I be worried?

My 17 year old daughter has had a chest/sinus problem for about three months and has recently been producing what looks like black hair from her chest/nose in phlegm. She originally had a bad cough and got antibiotics for a chest infection, the cough has gone but her sinuses are blocked and she still has a lot of phlegm in her nose and chest. She is a worrier and has researched the internet and has convinced herself that she has something more sinister. Please tell me what this could be, she is a non smoker in a non smoking envionment.