Fin rot wouldn't have done that much damage over night. One of the tell tale signs of fin rot is discoloration (black or dark edging) at the edge of the fins and I don't see any of that in the pics. It is more than likely the filter intake, or he is a tale biter. Add salt with your water changes, and make sure to keep the water extra clean to help prevent fin rot during healing. Some Betta Max or stress coat will help along in the healing process if you have any. Pretty boy by the way.
Mela fix is a very strong medication, and those of us here who do use it only use half the dosage. Some say it is not good for bettas though.
I like to use 3 or 4 drops of pima fix and 2 tsp aquarium salt/gallon for fin rot, then some betta max or stress coat to help it heal after the rot is gone. I use the duetto 50 submersible filter by marineland in my smaller betta tanks. They are adjustable flow, and the output can rotate a full 360 degrees so you can turn it right into the glass if you want. One thing you could do is go out and buy a brand new pair of panty hose, rince it really well in hot water, and cut a piece big enough to go around your filter intake. Secure it with a rubber band. That will keep him from getting his tail caught in there but you might have to change it every couple weeks once it get's all gunked up with all the stuff that would normally get caught in the filter meidia. GL! HTH!