Medical jellies, what is this pain in my chest?

Probably muscular, but it is possible to crack a rib coughing. Best see your doctor; he/she may want to do an x-ray.

It could be muscular. Honestly, sudden or new chest pain should always be checked out by a doctor. Wouldn’t hurt to find out for sure.

Of course I recommend you go to the doctor :) but you already know that so since I have had bouts of pneumonia and bronchitis my entire life and I just got through a bad case of bronchitis again, this pain is quite familiar to me.

It could be pleurisy

In my experience, I have needed antibiotics to help clear it up. In most cases, what I needed was codeine and cough syrup to help stop the coughing so my respiratory system has time to rest/heal.

Three people at work have had the extended cough thing, and have missed two weeks of work or more with pneumonia. One was hospitalized. You need to call the doctor. Did you have a chest x-ray.

As stated previously, go back to your doctor. I had a cold when I was very pregnant with my last. I coughed unexpectedly while I was turning to look back and ended up fracturing a rib at the back on my right side. The pain was intense. I could not lie down at all and had to sleep sitting up supported by pillows. Of course, then I had to convince the doctors that my SO did not abuse me causing a fractured rib.

Agree with @Dr_Dredd