He'll be fine :) Just watch out for the edges going black or grey, that's a sign of finrot. But otherwise you can get something called StressCoat, it's a conditioner like what you are using everytime you change your Betta's water. But it has aloe in it to heal the fins quicker, if you use that he'll start growing his fins back.
But the most important thing to do is keep his water clean and warm. So if you've got a heater that's one thing down! And then just keep up on your regular weekly water changes. What size tank is it?