If he's having trouble getting up I would say hip and leg x-rays would be common. You can see arthritis in x-rays, it is very plain as day to see the degenerative knee problem as well as the arthritis in my girl's x-rays. Now we had the original ones done and I won't be doing them again, but for a dog that age I wouldn't just jump right into arthritis. I would definitely talk to the vet about x-rays.
To be honest, if it were me I would find another vet. No doctor human or animal should be giving you medication without telling you what it is for and they should explain any possible side effects to you as well and also let you know if such and such doesn't happen then it's not working and give us a call. If that was not done that's not right IMO. Also they really shouldn't be RX-ing pain medication and anti-inflammatory medication without a diagnosis IMO.