Medical jellies, what is this pain in my chest?

I started with a cough almost 4 weeks ago, and went to a doctor last week. She diagnosed a sinus infection and put me azithromycin, benzonatate, guaifenesin, and dextromethorphan. For the last three days, I’ve had a sharp, intense pain every time I cough in the lower right quadrant of my chest, and now it feels as if someone has shoved a pry bar under my lowest rib and is attempting to lever it out of my chest every time I cough.

I assume that this pain is related to the duration and intensity of my coughing, but what is the likely physical cause of this pain? Is it muscular? What happens in cases of chronic cough?