How come when i cough a lot my back starts to hurt? but it only hurts when i cough for long period of time. should i be worried?

Increased pressure: Coughing causes increase intra-abdominal pressure. This pressure can be transmitted to the discs in the back. If there is disc degeneration or even herniation this could lead to some increased back pain. Coughing also engages the muscles in the lower back than can also become sore. I would see your pcp if the symptoms continue beyond the resolution of your cough.