I have an acute upper respiratory infection according to the doctor. why does my upper back and right shoulder hurts/sore when i cough?

Chest muscles can: easily become quite fatigued & soar from stabilizing your rib cage with recurring coughing. This is probably the most likely basis. Pleuritis, see: http://en.wikipedia.org/wiki/pleurisy is also a possibility & the list goes on & on. Study: https://www.google.com/#q=URI+chest+pain for additional ideas; yet caution to not let imagination/fears run away into rare, highly unlikely possibilities.