My 3 year old cat has urinary tract infection but how long will it take to get better?

The vet prescribed Clavamox, a relaxer to help my cat urinate better, and special prescription food (Royal Canin Urinary SO). I told the vet after 4 days that Clavamox hasn't done much for my cat from past experience. The vet said to stop using the antibiotic and just keep feeding him the Royal Canin Urinary food and he should get better. It's been over a week now and this morning, my cat urinated in my bathtub and my son's gym bag! He usually goes in his litterbox, so I know he's still uncomfortable with his condition. How long does it take for this UTI to go away??? I called my vet and left a msg but just wanted to ask your opinion. Does he need a stronger antibiotic?