Yes, your first step here is to test for CAE.
Now - there is a LOT of fear-mongering about CAE. If your boys are infected with CAE they are not dangerous to anyone. CAE is spread through milk - I have not one confirmed case of it spreading any other way, though many claim it can spread through sharing water troughs and contact. I have not found this to be true in my research. The majority live symptom-less lives for a good long time.
It is only contagious to goats and sheep (It’s called OPP in sheep).
Which medication are you considering? When I give banamine, I give 1cc per 100lbs (you can go ahead and give him 1cc) IM. We don’t use Adequan so I am not sure if the dosage is different.
If he damaged that knee, it could be part of the problem indeed. If you can get it under control most goats get along just fine with one bum leg, but goats do not generally handle pain well - something to keep in mind.