Maybe not the lung itself, but a muscle you have injured while coughing or pleurisy (irritation of lining between outside of lung & chest wall) or chostochondritis (irritation of cartilage attachment to ribs). I find that carefully stretching my chest and upper back several times a day relieves the pain.
I find that my pain worsens when I try to "protect" the area by minimizing motion. In pain rehab, I learned that regular, gentle stretching every day gradually loosens things up. As a matter of fact, today, after 3 crazy weeks of preparing for an art show and working on my bathroom, everything hurts. My body is yelling "Leave me alone. I just want to curl up in bed and sleep." But, I got up and am moving around slowly, stopping every few minutes to stretch & do yoga breathing. After 2 hours, I still hurt but am able to move pretty normally.
I would suggest that maybe a PT consult for some stretching and breathing techniques might help. Have you tried any exercises?
Sue