It sounds to me like he might have injured his swim bladder when he jumped out of the tank, given the location of the swelling and the issues he's having with buoyancy. The swim bladder is an internal, gas filled organ that fish use to control their buoyancy by adjusting the gasses within the swim bladder. It can be injured and/or rupture as a result of physical trauma, such as a fight or a fall.
The swim bladder is a fairly large organ relative the fish, and stretches down the last 2/3rds of a betta's body, parallel to the spine. Here's a link to a diagram of a betta's internal organs, showing the swim bladder:
Here's an article that discusses swim bladder disease, which sounds like the problem that your betta is having. Note that swim bladder disease can be caused by injury and constipation as well as bacterial infections, which are less common.
Since the betta is eating and behaving normally other than the swelling and floating issues, I'd continue to feed him so that he has the energy to heal any damage to his swim bladder and inner tissues. Epsom salt might be a good idea to lessen any swelling. Do NOT use aquarium salt though, as that will make swelling worse. Here's an article that talks about dropsy in fish, and some things that can be done to reduce swelling, as well as the specific dosing for Epsom salt:
The fish may be able to heal a swim bladder issue on his own and be back to normal! (here's hoping!). I might hold off on treating for a bacterial infection for a little bit, since antibiotics and other medicines are hard on fish while they're in the water. But watch the fish very very carefully for signs that he's getting worse or simply that he's not improving, as I'm not sure if an infection could result from an injury, like what might have happened to your fish when he fell.
Sorry for the info overload, but that's my best guess as to what's going on and I hope it's helpful!
Wishing your fishy a speedy recovery! :)