Could a cough lead to upper back pain?

Yes. Most likely secondary to muscle strain or if cough is due to pneumonia, then pleuritic chest or back pain depending on part of lung involved.
Yes. A persistent cough could cause a pulled muscle in back muscles or in the muscles in between the ribs. This will definitely cause pain.

Related Questions

Left upper back pain while breathing in and couging? Also had dry cough for 2 weeks. Only 17

Option: Chest Xray. This usually shows may be you have some problems in the lungs due to possible viral or bacterial infection. May be you want to check with chest xray.

I was coughing and now I am having upper back pain when I breathe, cough and move? Is it my back or my lungs.

Productive cough? If you are having productive sputum (cough) that's not relieved by your otc meds, it's time to see your doctor for a lung exam, (and possible chest xray) to rule out an uri, from walking pneumonia, depending on other factors /symptoms (fever, chills, etc). They may have to start you on antibiotics if warranted. Since your lungs are involved, it can affect your uppoer back if you cough a lot.

Upper back pain, feels like I've got a constant cramp for 3 days now. Uncontrollable coughing and pain in chest too. What should I do to stop cough?

Visit your doctor. I am concerned about you. Where you are now is manageable but would not want you to get any worse. You should go say hello and let them make some recommendations. Best of luck!