Betta's Fin rot not Getting better

[Fish123]

I got him from PetSmart a few weeks ago. I noticed that he had minor fin rot so I did 50% changes and added double dose of stresscoat. However, that did not work and it got worse. I added some salt (1TSP/G) and did 100% daily. His fins kept melting away and so I shut off his heater and filter to see if that'll make a difference. Unfortunately, the next morning, HALF of his tail was GONE. I couldnt wait any longer and picked up some API T.C. Tetracycline, it was the only medication for Fin rot that I could find (other than betta and metafix).

His fins are still melting away.
He is in a 5 gallon tank by himself.
Not cycled but i have been doing 50% changes everyday.
72F, internal filter is off, no carbon.
I use Seachem Prime, but swapped to StressCoat to help his fins grow.

The first photo was from yesterday morning. The second is from last night, and the third was today. I put a mirror beside him to make him stretch his fins out so that I could see them properly.

How do I tell if the Fin Rot is gone?? His rot is not getting any better

 

[shellyx]

I would just be giving him clean water without meds. His temp seems a bit cool too me, my bettas is 80 as they like it warm.
Is there anything in the tank he could be ripping his fins on? Or has he been biting his own fins?
Keep up 50 % daily cleans with treated water and match the temp to his tank water.
Is his filter gentle?
What are the parameters?

 

[Fish123]

I would just be giving him clean water without meds. His temp seems a bit cool too me, my bettas is 80 as they like it warm.
Is there anything in the tank he could be ripping his fins on? Or has he been biting his own fins?
Keep up 50 % daily cleans with treated water and match the temp to his tank water.
Is his filter gentle?
What are the parameters?

I've already tried that. It got worse after 5 days so I started to add salt. I read that the cooler temp would help keep bacterial growth at minimum. His filter is a cheap tetra internal filter, and has some plants near the output to weaken the flow. I've had bettas in the past and their finrot healed just fine with clean water. This betta's finrot is extremely agressive. His fins melted slowly at first, and one morning, half his tail was gone. That's when I resorted to medication.
Everything is 0PPM, PH is about 7.