Could Cough Be Due To Kidney Stone Reformation?

I have had a really bad cough for the past week with no signs of infection -- no congestion, no fever, no sinus pain. It's a post-nasal drip type of cough. I had this same cough last June and when it didn't go away, tests showed I had a UTI (with no symptoms). Took an antibiotic and a month later still had the UTI (again with no symptoms). Was sent to a urologist and, after a KUB CT scan, it was found that I had a very large kidney stone. Urine culture showed the presence of proteus bacteria generated by this stone. I had surgery to remove this stone (actually three procedures) and, though I am not totally 100% stone-free, the urologist was happy with the outcome and a CT showed only fragments remaining. Could this cough once again be a sign of stone formation that is producing the Proteus bacteria? A course of Z-pack since Friday hasn't even touched the cough.