I had a dog with a sprain. It was hard for about two weeks we had to monitor him. Basically we blocked all the furniture so he couldn’t hide under it. He didn’t like not having a “den” anymore. He could get under it but not get back out.
Then outside was strictly a leash or tied to a tree. He had a huge backyard to roam in so he was not happy, but if it is a sprain, it’ll heal but you just have to restrict kitty’s behaviour. They won’t like but they have no say.
I would suggest a harness for the cat and keep him on it till he gets better
As for spraining a leg? That is so easy to do. I once got a wallop of a sprain leg simply by stepping off a bus wrong. I said "ouch, then kept walking, by the time I got to work my leg was swollen up twice normal size. Simply stepping on it at a bad angle can do it
Where’s his pic?