Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear about Reily being uncomfortable.
Did the previous medications help?
If so ideally he would wait to see his veterinarian because the prescription medication your veterinarian has for pain will be much safer and work better than any over the counter medications that we take. In fact acetaminophen and ibuprofen aren't used in dogs because their effective doses are very close to a toxic dose in dogs.
The only over the counter anti-inflammatory that can be used in dogs is buffered, enteric coated aspirin (like ascriptin). Aspirin does cause stomach and intestinal irritation and ulceration as well as clotting problems so should not be given for more than 2 to 3 days consecutively and should always be given with a meal. If you choose to use it watch for lack of appetite, vomiting, blood in the stools or dark tarry stools and stop immediately if you see those. Do not use aspirin if your dog has liver or kidney disease or a history of a sensitive stomach or clotting problems. There should be a 5-7 day washout period between giving any nonsteroidal or steroid and nonsteroidal anti-inflammatory. If given too close together then the odds of causing serious side effects are much higher.
If he seems miserable though the dose for aspirin is 5mg to 10mg per pound of body weight orally every 12 hours (about one half of a 325mg aspirin for a 25 pound dog every 12 hours). Always give with a meal. Do not use for more than 2 or 3 days.
Be aware if you choose to use aspirin and it doesn't help your veterinarian will be limited on what they can give because there must be a 5 to 7 day washout period between different nonsteroidals or nonsteroidals and steroids.
You can try alternating warm and cold packs on his painful areas for 10 minutes at a time several times a day.
Make sure to rest him, no running , stairs or jumping.
Long term for joint pain I recommend using a combination of a glucosamine/chondroitin product (examples are Dasuquin or Cosequin) and an omega 3 fatty acid (like 3V Caps or Derm Caps). I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give him 20mg of EPA per pound of body weight per day. For example a 25 pound dog could take 500mg of EPA per day. Omega 3's and glucosamine/chondroitins work synergistically and improve cartilage health and joint fluid quality and quantity as well as reducing inflammation. They can take several weeks to see full improvement but some dogs do very well long term with them alone after an initial course of anti-inflammatories. They are available over the counter.
Another option is a product called Duralactin. This is an anti-inflammatory product derived from milk proteins and it also has omega 3 fatty acids incorporated into it which can be very helpful. See this link for further information: http://www.duralactin.com/products_canine.htm
If the compresses and exercise restriction are not enough you can try aspirin, just make sure to tell his veterinarian when he sees them.
Perhaps a different prescription anti-inflammatory will work better for him rather than the first one that was prescribed. Veterinary nonsteroidal drugs we can use include a nonsteroidal like Metacam, Deramaxx, Previcox or Rimadyl. If those aren't enough we can add another drug in the opiod family called Tramadol and/or another drug called Gabapentin. These drugs are much safer and more effective than aspirin. Aspirin used for any length of time will create gastrointestinal ulcers and clotting problems.
Best of luck with your fellow, please let me know if you have any further questions