I've dealt with arthritic dogs for several years. Rimadyl worked very well for many years on the dog with the worst problem. After that, a new med called deramax came available and worked wonders for him. We also use it on our shepherd mix with great results, but it's probably the most expensive dog anti-inflammatory out there right now.
Another prescription med is etogesic. None of my dogs could tolerate it. With the first dose it caused vomiting and loss of appetite and then diarrhea.
Glucosamine and MSM are great alternatives as well, but as already noted, it takes some time to really get working. Some of the commerical foods for Senior Dogs contain both glucosamine and MSM so read some packaging labels and try changing to one of these brands.
If the arthritis is bad enough, you can also consider steroids, but be aware they have their own set of problems with some dogs. It just depends on how bad the pain is and the individual dog, so you're in for some experimenting to find what will work best.
Don't forget that regular walking really helps too. If your dog is rarely walked, try to start out with 10 or 15 minutes a day and work your way slowly up from there to 30 minutes twice a day. If you have access to a pool or a pond, swimming is even better. The more muscle that is available to help support the joints, the less stress is put on the bones to do all the work. Having a regular daily walking schedule really helped my severely arthritic dog not only physically, but mentally - and me too! :-)
You might want to look into learning animal massage. It worked wonders for my horse and my dogs.
Yes, you can also call the vet and they can try another med that may work better. My dog could take rimadyl, but not the previcox.
I have had great success with Glucosamine with MSM.. That will take a few months to kick in, but once it does, is wonderful and safe. Unless your dog has been on that, and it is not helping.
I buy SyoviG3 soft chews, my dogs love them, think they are treats.
Do a research online google the medication that your vet subscribed for you and see what side effects come up. You will see how the nsaids react on some dogs..
Did your vet do any blood work on your dog before he gave you any medicine?
What medicine did he prescribe for your dog ?