Although having parents that went through cancer put you on a higher risk in getting one, it is not enough to conclude that your cough has any relation with it. It may be said the cough is also a symptom of a lung cancer but it is a prolonged one. It has only been for a few weeks try giving it more time. If it still persists consult a doctor.
If you don't want cancer, don't use prednisone. To help your cough, use mint tea, bone broth, Nigella sativa, hemp oil, things like that. For your body ache, take magnesium citrate (use another form if you can't have your bowel movements speed up) and zinc gluconate to help get over a cold virus.