If the cat is two years old or older it is an adult cat. If it's still under two years of age it is still considered a kitten. My suggestion to you (since having worked for vets as a vet tech myself) would try just half of a buffered aspirin. Buffered is a coating like Advil that won't hurt there stomach.
Start with half a pill. If still in pain then give other half. Best waiting period for the other half would be two hours. Not all vets are correct for I have come across a few that were wrong. Many do need to go back to school as a refresher. I'm not putting any of them down I respect the work they do, but there are new breakthrough's with animals and what they can or cannot handle.
I hope this helps. Remember any cat/kitten over 6 months of age I would give 1/2 buffered aspirin every 2-4 hours even stretching it to every 6 hours. You don't have to give them too much cause it will in the end cause liver, kidney, and spleen problems, as well as stomach and heart problems if exposed for long periods of time. Good luck and I hope your kitty feels better soon. Oh I almost forgot. Another good thing to do is, depending on where the pain is, a nice warm compress or heating pad set on low-med. could also help sooth the pain. Again good luck :) and best wishes from Annie The Pet Nanny.