Having a CT scan for humaturia little discomfort when urinating?

Depends. A ct scan done for hematuria is typically for kidney, ureteral or bladder stone. This is typically done without contrast. A ct with contrast will also help with evaluating for possible tumor along the urinary tract, including the kidneys, ureters or urinary bladder.
CT primarily stones. Ct for hematuria is to assess for renal or ureteral calculi. Once that is excluded and symptoms persist, then ct or mr urographic study to assess for lesions intrinsic to the ureters and renal collecting systems.