Can you shine a bright light on him and see if he possibly has ick? Even if he's not ripping around the tank scratching himself often times ick makes the fins go all clampy. And the reason for the light is because occasionally you can't see it with normal lighting.
It doesn't appear to be fin rot and it's clearly not tail biting, here are acouple photos to show:
Fin rot (you can see the lace look at the edges of the fins: https://sphotos-a-sjc.xx.fbcdn.net/h...87755212_n.jpg
Tail Biting (all the jagged spikey edges): https://sphotos-a-sjc.xx.fbcdn.net/h...62216789_n.jpg
I always recommend using Aquarium Salt before trying any medications, simply because most things can be cured with some salt and fresh water. If you had a fish who turned black and died after adding salt it honestly was probably something that was horribly wrong with the fish and he/she just happened to have had the last straw and died.
It's 1 teaspoon per US gallon. If you can find it get API Stress Coat+ and use that as your water conditioner from now on, it's by far the best water conditioner to use on sick, possibly sick, or stress easy fish (I've used it for years and use it for my normal conditioner). It's very possible that its your water conditioner that has caused this problem, bad bottles or expired products often create problems like this. Keep the heater on, and do daily water changes. Hopefully you'll see and improvement soon.
Having a healthy diet can also help him get better faster. New Life Spectrum for Bettas is excellent nutritious food, so is the Small Fish Formula if he ever happens to get bloated from normal foods. Frozen Glassworms would be an excellent food to feed him too, as frozen or live foods are the most nutritious. Keep away from Brine Shrimp and Daphnia for now though, even though they are good for the fish they aren't meant to be a every day food as they both are natural laxatives. Also remember to not feed any Bloodworms right now either, they have 0 nutrition and shouldn't be fed to a recouping fish.