If you sprain your foot, you can get rather massive swelling and it will linger for quite some time. The swelling can actually be worse with soft tissue injury than with a broken bone. Soft tissue injury can be really bad if ligaments have been severed.
Treatment of a broken foot vs a sprained foot is different though. A broken foot needs rest, it should not have the pressure of the body’s weight on it until it has healed. A sprained foot should as a rule be walked on. So it’s a good idea to have x-rays done to see if if you need to cage him to restrict his movements for the next few weeks.
A broken bone or a bad sprain is sometimes treated with a cast or splint, if the break is considered unstable or the sprain is causing lots of swelling. Many rabbits wont tolerate any sort of band aging though, so you may need to keep a cone on him for when you cant watch him.
It’s very good you have a painkiller for him. It’s very important. Rabbits are highly sensitive to pain and pain can make them go off their food, which is dangerous.