Zen, Angelic and Dr are all right!
Bettas, due to massive breeding for the last couple of hundred years, are much more susceptible to diseases.
And breeding for long beautiful fins has actually made a fish that can not fight water current as well as a naturally spawned betta.
I believe that you should do as was already recommended and use a filter that makes very little water flow.
Your little betta was scared by two things : 1) change in his environment, and 2) faster water flow.
Stress causes bettas immune systems to slow down, and the microscopic bacteria that is in your tank then attacks, and causes any number of diseases.
And YES, get some aquarium salt, NOT TABLE salt, and use a salt bath to treat your betta while you let the filter assimilate the tank water for at least 24 hours wth your betta out of the tank.