They will grow back. It will take time, several weeks, but when it starts to grow back it will be whitish growth starting at the point closest to the body.
Fin rot medication probably won't do much. What you could do is add a small amount of aquarium salt to help keep the water clean and prevent infection, which will promote new growth. I would say 1 tsp per gallon of water in the tank, there's no need to use a huge dose.
As a side note, examine the tank and divider very closely to make sure the divider really was jumped. I thought that I had a jumper once only to discover that one of the fish was actually sneaking through a hole I thought was WAY too small to squeeze through near the surface where I had cut the divider to make it fit.
If it really did jump the divider, you can attach another piece of mesh (or cardboard, or anything that you have) horizontally over the top of the divider so it has a "T" shape. That way the fish would not only have to jump UP to make it to the other side, it would also have to jump OVER several inches to successfully make it to the other side.