it seems like his tail more than shredded, i think you might have trouble seeing the "burnt edges" of fin rot because of his color. i would say its fin rot. im highly assuming you have no plastic plants? it
could be fin shredding (as in from swimming past a plastic plant) but i would strongly think its fin rot. (it looks like too much tail is gone and not just ripped) i initially had both of my bettas in a divided tank, mr teal got fin rot, but mr purple didnt. (and hes still fine (knock on wood!)
at first i treated with jungle fungus eliminator 1/4 tsp per gallon and aqua salt (1 tsp per 1 gallon) hes in a 1 gallon betta tank. whatever you do dont stop the treatment early, i did that thinking he was ok and he had 2 relapses! (i think giving whatever medicine your using 1-2 weeks minimum) i have now moved onto kanacyn. (i have been told its great for stubborn cases of fin rot) the actual rot has stopped but there is some shredding going on, but its happening where the fin was bloodied a bit (both my bettas are pastel colors BTW so its easy to see anything like this on them)
i think the melafix will help but dont over medicate as the tea tree oil can have adverse effects on the labyrinth organ (or so some people say) i have only used bettafix as far as a tea tree oil treatment is concerned (thats the metacula (sp?)stuff in the "fix" products) its a natural antiseptic etc, but its used a lot for people. (for cuts, acne healing etc) but it is supposed to assist in fin healing and regrowth. my water change schedule (while using kanacyn, but im sure you could do something similar)
day 1- 50% water change add meds, day 3- 50% water change add meds, day 5- 100% water change add meds and then begin again on day 7 with 50% and so on. this is in a 1 gallon tank BTW, but im assuming you have moved him to a hospital tank (that would probably be small). i also use amquel (for ammonia removal) and novaqua.
the first place mr teal got the fin rot in does have some new regrowth, in the fin and ray this is about 2 weeks later. so since youve started with the melafix keep on with that and see how it goes.
good luck with him!!