I have been coughfing a lot due to a common cold , now i feel a pain in my upper back of chest coul be that muscular or.my right side lungs ? please.

Muscle contraction: The term "cold" usually refers to a rhinitis or inflammation of the nasal mucosa. Although i believe this is a viral infection, the cough is most likely a bronchitis. The pain in the back of the chest is most likely muscle contraction and unlikely pain from the lungs. If the symptoms do not clear up in 2 to 3 weeks, a chest physician or pulmonologist should be consulted.

Maybe/not: People with upper airway congestion & cough brought on by viruses can develop secondary issues that are more worrisome. Pain that only occurs with a cough may be from the muscles between the ribs if sprained. However, more constant pain may reflect a signal to a localized pneumonia near the lung linings triggering a dull constant pain. If this is more than your regular "cold" get it checked out.