Vet here:
Really surprised you didn't see much improvement with Carprofen. Could be the dose wasn't appropriate. If your dog had anaplasmosis, that could potentially be a aggravating factor as well. Tick borne pathogens do some funky stuff.
I generally use Galliprant for dogs that have GI sensitivities with Carprofen or other similar NSAIDs. I'll also use Galliprant in dogs with mild liver/renal issues as it's generally safer on those organs for long term use. I haven't been overly impressed with it's effectiveness with the majority of patients that have been put on it, but it's better than nothing.
The Librela injection is going to be huge once it's on the market. Our clinic is supposedly going to get it sooner than most clinics for clinical trials, but don't know when that will be. We have the product for cats which blocks the same cell signaling protein (Nerve Growth Factor) from binding to it's receptor. By doing so it prevents further inflammation being stimulated within the joint. It does a great job in cats and I've had success with treating other issues off-label (urinary bladder inflammation from stress).
May want to get some rads and lab work done to make sure there isn't anything else going on.