It could be dropsy. The cause can be viral, bacterial, fluid building up due to old age, a tumor - there are many possible causes. The scales don't always have to stick out when dropsy occurs. I had a betta live for 10 days in a very swollen state. He ate and was active until the 10th day.
Here are some of the things I did - they ultimately didn't save him but I hope I made his last days more comfortable.
In a QT
tank, use 1/8 epsom salt per gallon, to try to draw the fluid out. Add maybe 1/2 of that amount, and then a few hours later, add the rest. The next day, you can add just a pinch more. If that doesn't seem to help after a day or two, do about a 60-70% water change and try an antibiotic. I have used Jungle Fungus Eliminator and Kanaplex (Seachem) on my bettas. There's a new liquid antibiotic from Mardel that says it treats dropsy. I've used it for finrot with success but not dropsy.
You can also try to feed the Kanaplex. Put a little bit of tankwater - a tablespoon or two - into a plastic cup. Put a pinch of Kanaplex in and dissolve it. Put some freeze-dried bloodworms in to soak up the medicine water for about 5 minutes, and then feed to the betta.
Finally, you can try to feed a pea. Peas can clear out digestive blockages, but usually you feed the pea weekly as a preventative measure. I boil frozen peas in the microwave for 4 1/2 minutes. I don't bring the water to a boil first; I just fill a glass with about a half cup of water, add peas, and heat on high for 4 1/2 minutes. Let cool - peel and throw away the skin. Use a little paring knife (yes, it's tedious!) and cut small pieces of pea to match the size of his regular food. I use a plastic spoon to feed the pea. Since the pea pieces will probably sink, I get the betta's attention with the spoon (they know it by now!) and when they come up to it, I let the pea float off, and the bettas usually catch the pieces quickly before they sink.
Hopefully some of these things will help. Good luck!