Well, I can honestly say nothing over-the-counter is really that safe or that effective.
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, Ibuprofen (Advil), and Aleve safe.
You can give 10mg per pound of body weight up to every 12 hours. Just remember, there are different pill sizes for aspirin, so look to see if it is an adult pill, extra strength, etc.
Aspirin can be upsetting to the stomach, so discontinue if any digestive upset and definitely consult a vet if not helpful.
***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. Severe stomach 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***
Certain soft tissue injuries can heal. A ligament tear will not heal.
Fractures can sometimes heal if properly stabilized (cast/splint), whereas, if the broken bone fragments are displaced far apart, they will never heal correctly.
Some fractures require surgery (pins, bone plates, etc..). Some require splints for about 6-8 weeks.