Aspirin is NOT good to give dogs long term, very hard on their GI system. One of our geriatric pups ended up with a bleeding ulcer from giving it (at our then-vet's advice)
She was a cute little mutt (American purebred) & suffered from arthritis in her back & hip dysplasia. We wanted her to be as comfortable as possible, & working with our vet, decided on a regimen of Tramadol (brand name Ultram)
It is a strong analgesic drug (pain reliever, not anti-inflammatory) & it helped us get another 2 years with our S. girl
You need to be more assertive for your dog when you talk to the vet. Do some research online & come prepared with possible medications & treatments, & ask to discuss the pros & cons.
In addition to the drug I mentioned above, there are anti-inflammatory meds (Rimadyl) and more holistic treatments (cold-laser therapy does wonders for arthritis).
If your vet is not willing to work with you on different, more beneficial treatments, then be prepared to walk. Your dog is depending on you to be his voice. Good luck. T.