What dose did u used with the Meloxicam? It's also used in cats and horses.
Meloxicam is a selective Cox-2 inhibitor very similar to Celebrex.
Naproxen (Aleve) is a Cox-1.
Cox 2 are safer for the gut and not as corrosive to stomach lining as Cox1 like naproxen. Though IMHO naproxen is a better pain reliever than Meloxicam or Celebrex.
You will be familiar with the term NSAID I am sure, and that is what they are.
Tylenol (acetaminophen) is not an NSAID, as it doesn't reduce inflammation. But it is good for minor pain and fever relief .
Other pain meds will fall into opioids like codien, tramadol, etc. Effective pain relief but prone to habit forming, and also the longer they are used the less effective they become

. They act on the central nervous system, but don't reduce inflammation.
And all meds come with their own issues. It's no wonder pain control is such a huge thing!