AQ Salt will probably do a good job here. Generally for external problems, one should start with 1 teaspoon/gallon of AQ salt for 7-10 days, changing the water (and adding salt) every single day.
Make sure to PRE-MIX the salt before putting your betta in. As Myates pointed out, Start right and Stress coat are the same thing, but I personally prefer Stresscoat+ which has aloe in it. It will promote slime coat production (to shed the excess) and promote sanitary healing for his fin loss.
I recommend making your next purchase to be a heater. Having warm water does worlds of good for their immune system, similar to you catching a cold and having a warm blanket vs. standing out in the cold.
As for IAL, you can use it if you want, I don't really think it is necessary.
I hope he gets well soon.