I have pain in my upper back on the right side. Could there be something seriously wrong? What serious conditions?

Not likely. The upper back is a common area for muscle tension. Serious problems would be cervical or thoracic discs with referred pain or referred pain from internal organs.
Many things - possib. Possibly serious. Heart/lung/musculoskeletal are most common. Can you breathe deeply and comfortably? Any nausea or shortness of breath? See a doctor right away.