You may be forgetting or not realize the extent to which metabolism, effects, and side effects of drugs differ between species - absorption, distribution, excretion, receptor binding and selectivity (including COX selectivity), toxicity, etc., all depend on species. Even for similar situations, the NSAID, antibiotic, etc., chosen for a human is likely to be different from that chosen for a dog, which is different from that chosen for a cat or horse or cow, because the average risk : potential benefit ratio for each drug differs between species. That's why vet school is different from med school and why human medical professionals should not attempt to treat animals when there is veterinary help available, and vice versa.
I'm also not sure why you want to ignore the advice of the veterinary professional you paid to treat your dog so that you, knowing virtually nothing about veterinary medicine or veterinary pharmacology, can make your own treatment plan with the help of strangers on the Internet. As stated above, if you don't trust your vet, get a second opinion.
BTW, carprofen appears to be somewhat COX-2 prefential in dogs, as opposed to other species in which it is non-selective.
Good luck with your dog.