Picking fins?

I initially bought my Betta the second week of January. The tank was fully cycled. I had bought him from PetSmart and I saw he had minimal fin rot so I just made sure the tank was comfortable for him and well cycled. I was pretty sure I had gotten rid of the fin rot. About a month later I bought 7 neon tetras and ended up trading them for golden mountain minnows because my Betta was being picked on by the neons. He was a bit torn up after the neons. It's been about half a month to a month that the neons have been gone but my Bettas fins don't seem to be getting better.


It's hard to get a good picture of him, he's always moving.
His fins seem to be getting worse. I don't think it's fin rot. The water parameters are all at zero, my filter isn't strong, the decor is all betta proof. He has a ship decor with holes in it but I deemed the inside a little too dangerous so I blocked all the holes to get in.
Is he picking his fins, or is the fin rot back? I've watched the minnows for hours and they keep to themselves.
If y'all need a better picture I can stalk him some more.

 

The Fin Rot is back. You can tell by the discoloration and melting fins. My Betta has Fin Rot right now too, and I was told the simplest treatment is 25%-50% Water changes every other day. All my water parameters are at 0ppm and Nitrate might be between 0-5ppm, but my Betta still has Fin Rot. It seems our situation is similar but if you could provide the tank size and temp that would be helpful.

 

Temp shifts between 76-80
There is 10 gallons
Also, there are real plants

 

How many Minnows are in there?
This still seems like Fin Rot to me. Good luck.

 

There are 3 minnows. I was a little sketchy at only buying three but they are hyper and happy. Thanks for the help. I'll have to try the water changes. I can't really go out and buy medication with everything happening nowadays.