Why does the right side of my back ache when i cough?

Pain in the chest (front or back), especially if you have been ill and coughing frequently can indicate lung involvement such as pneumonia or chest wall muscle strain (costochondritis). You should see your Dr and get a full examination including having them listen to your lungs, and blood tests.

I agree with Dr. Kratzberg, although back pain is more often associated with muscular strain from coughing than with pneumonia. Costochondritis is inflammation of the cartilage around the ribs, possibly from a virus rather than from coughing. Even though it may just be muscle strain, please see your doctor to be evaluated to be sure.