Welcome! My name isXXXXX am a 2003 graduate from UC Davis, and currently a Medical Director of a veterinary hospital.
I am sorry to hear about this concern for Nanook.
Well, one of the most common symptoms or complications with just about ANY of the non-steroidal anti-inflammatories is vomiting or diarrhea.
I would absolutely have no reason to assume that this is a sign of liver distress.
Of course, if the stools were to get worse on the medication, you'll have to stop and switch to a different anti-inflammatory.
Since you mentioned severe arthritis, here is a bunch of info about the most popular medications vets use:
A few common medications prescribed by vets (not all options,but many of the most common choices): NSAIDS,RimadylDeramaxxMetacam
Currently, one of my favorite joint support supplements on the market is Dasuquin or Cosequin. Here is some more information about it. Many veterinarians and clients have observed that after a few months on a quality joint support product, they can often reduce the dose of the non-steroidal anti-inflammatory medications there pets may already be taking. A supplement can take several weeks to observe benefit, so it is important additional anti-inflammatory or pain medications are used in the meantime. Product Information about Dasuquin / Cosequin
Also, an incredible clinically tested food to help with joint problems is J/D. J/D Diet
Another supplement to review would be Adequan injections for joint health. These injections are also quite popular and have helped many pets with arthritic disease. Adequan injections
I hope that information has been helpful.
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