I was sick 3 weeks ago, my cough never went away i was on z pak yesterday i started coughing green stuff again runny nose and sneezing. lung cancer?

Unlikely: At your age it is much more likely you have a recurrence of your prior illness or a new infection. Take measures to treat your symptoms and if not improving within 24/48hrs get a culture of your mucous done as well as consider getting a chest x-ray if problems persist. May also want to wear a mask to protect others till you are well

I would not jump: to conclusion that you have cancer. It is most likely an infection. If you don't respond to medications - then let your doctor know.