No...tylenol is not recommended, and neither is ibuprofen.
The only over-the-counter would be aspirin.
The only over-the-counter non-steroidal anti-inflammatory I recommend in dogs (NOT CATS) is aspirin. Due to potential toxicity issues if not dosed correctly, many veterinarians do not consider Tylenol or ibuprofen (Advil) safe. You can find the dose for aspirin in the following link:
***Do not give aspirin or any other non-steroidal anti-inflammatory medication if your pet is already on prednisone or any other anti-inflammatory medication***
and intestinal ulcers can result from giving a pet aspirin, Tylenol or ibuprofen when they are also on medications like Rimadyl
, Deramaxx, Prednisone, Metecam, Zubrin, and Previcox
However, I am assuming you are asking because your pet is uncomfortable, or is limping. She would probably benefit MUCH MORE from a good non-steroidal from your vet which is much more effective than aspirin, as well as, a good oral pain medication like Tramadol.