Aquarium salt has a specific use, and that is as a healing agent when your fish has damaged fin tissue or another kind of open wound. Many tropical fish, including bettas, come from areas of the world where the water has a very low electrolyte (salt) content, so adding salt to the water unnecessarily means their organs have to work harder to purge the excess salt from their systems. This extra pressure will wear down the fish's organs over time, so it is not advised to use aquarium salt for more than about a week or so as a treatment. I believe the medicinal dosage is 1 tbsp per 5 gallons.
Bettas are a rather hardy fish, since they have been extensively bred in captivity and they have scales to protect them. Other tropical fish like scaleless catfish (cories, otos, plecos, etc) and neon tetras, for instance, do not tolerate salt at all.
I suspect in this case there is more going on than just the salt, perhaps whatever factor that prompted the OP to use the salt in the first place plus the fact that, perhaps, the OP dumped the salt in a bit too quickly caused this extreme reaction in the fish. Hopefully the water changes will help.