I personally do not recommend western medicine because it only treats the symptoms but does not heal whatsoever. It appears that you potentially could have some unintended side effects from the naproxen. I would look to see what side effects this drug has and see if any are related to the kidney. And if this is a side effect, I personally think it would be silly to take a different drug to deal with the side effects from a seperate drug.
I would determine what organ could be causing the pain via testing and go to a naturopath who will heal this instead of prescribing medications.
Kidney pain is typically felt in the back as well so it could be a different organ.