Hello and thank you for your question.
It sounds like you have the flu
. This is a rather common virus that should be monitored to make sure that you are recovering from it. Certain strains can be dangerous. The popping is from the coughing and it's the intercostal cartilage
that is moving from the force of your cough. I would recommend getting an evaluation and check up from your doctor. Many different "bugs" can portray similar symptoms.