My son has bumpy skin on his arms/legs after a few days of on and off fever. Some of the bumpy area were itchy also. He also has cough. What's wrong?

Gianotti-crosti. It could be Gianotti-crosti, which is an eruption of red-purple spots, usually on the arms and legs that is often seen in kids who have or just had a viral illness. Another possibility is Keratosis Pilaris which shows up as bumps on the backs of the arms and sometimes on the thighs and often gets worse when kids are ill.
Hard to say. w/o more info, I would guess is that is a viral exanthem, which are harmless rashes caused by viral illnesses. Another possibility is something called acrodermatitis, which is a skin rxn against viruses and in some cases vaccines. Also harmless; antihistamines and steroid creams (like hydrocortisone), calamine lotion will help with the itch. The rash should resolve on its own.