yes, rimadyl is not a sulfa drug.
tramadol is not an NSAID.
and etogesic is not an enteric coated aspirin.
You saved me a lot of typing. As far as sulfa drugs go--you don't really need to know exactly what the mechanism is that causes reactions you just need to know that Dobes (and a couple of other breeds) are more likely to react to sulfa drugs than other breeds.
Sulfonamide allergies are common--I'm allergic to sulfa drugs.
Some sulfa drugs are more likely to cause allergies than others. Albon, which does have a sulfa radical generally doesn't caused problems--it's been prescribed and used without incident on several of my Dobe puppies who had coccidiosis. Metronidazol also has a sulfa radical and the only adverse reaction I've ever heard of with it was on a non-dobe.
The biggest offenders are the antibiotic sulfa drugs: "In people with adverse reactions to sulfonamide antibiotics, all other sulfonamide antibiotics should be avoided. These include trimethoprim-sulfamethoxazole (Septra®, Bactrim® and generics), sulfadizine, sulfisoxazole, and dapsone."
There are a number of other so called "non-antibiotic" sulfa drugs but in general because it is known that Dobes tend to be more likely to react to sulfa drugs the recommendation is to avoid them.
Incidental information: While I had a dog who lived comfortably for his last three years on EtoGesic I had another who had an instant and frightening reaction--one pill and he was pooping frank blood. The best protection when giving meds to any dog is to make sure that you are familiar with possible reactions so that you don't continue to medicate a dog with something that is causing problems.
The dog who reacted to the EtoGesic had degenerative disc disease in his later years--he was on low dosages of tramadol for several years for that. It can be given in conjunction with NSAID's and often is for dogs with very painful things like osteosarcomas.
As always--all of this should be discussed with your vet--there are often reasons why one drug is given in preference to others and there are drugs which should never be used in conjunction with others.
But not all vet know all of the breed specific potential problems--so I try to go armed with what I've learned in 50 years of Dobermans and if I don't recognise a drug I ask for the literature and I've turned down a couple of sulfonamides that were prescribed and explained why. Some vets know and some don't--most that I've dealt with are glad to hear about breed specific problems and change meds accordingly.