My back hurts when I sneeze or cough now. It didnt before today. I have been getting over a cold. The back hurt when I accidentally swallowed some water in the wrong pipe ( I am male). Now it is doing that when I have a strong cough or strong cold... but not always. Should I be concerned
First you need to take proper treatment for your frequent cold and cough.  It could be related to your immunity which may not be good.  And then do some spinal strengthening exercise.  Because if u have back pain while cough and cold then it shows your spinal muscles are not so strong to take the jerk when you sneeze.  And do check on your work posture as well as your normal sitting, walking standing posture.  Take care.