It can take longer for your lungs to recover. I have asthma and get a burning in my lungs from coughing a lot. I would just leave it for a few more days, unless you get worse or start coughing up grey mucus or hear a cracking noise when you breath (those are signs of pneumonia).
an aftermath of a cold is feeling better. burning and chest pain is not good. you would know if its bruising from coughing, it will feel like a tender tug ache hug where u cough. it shouldn't burn. u should go back.. or better yet.. go to urgent care that what and extra fifteen buck visit? they have cat scans and xrays at those places usually. you can't play around when u have copd.. you don't want to be in sepsis and not know it..
i was a little concerned actually not of your lungs but for heart. inflammation of the heart can act like your symptoms. if let go just a day or two too long sometimes is unrecoverable. lost my father that way. i think its called pericarditis. or something like that. if u have insurance, u got nothing to lose.