My kidneys hurt when i cough. is this the sign of an infection? what else could it be?

Possibly: The kidneys reside in the flank position and when one has flank pain it could be from a renal origin or could be musculoskeletal. A urinary tract infection would often have frequency urgency and dysuria. A kidney infection would often have associated fever and chills as well. A urine specimen for urinalysis as well as a culture would be important to have performed as well as a possible renal ultrasound.

Probably not...: Hurting in back at coughing alone usually suggests backache from musculoskeletal causes, not urinary infection. If any doubt, see an expert. But you go, record the features of pain in term of its onset, intensity, duration, interval, and other related matters to ease or worsen the pain. Good luck.