Betta Is Shedding, Listless- Please Help!

[Oriza]

I don't think it's fin & tail rot, because there's no blackish/burnt-like parts of the fins. But I got this betta from a local fish store about two days ago, where the other fish in the tank seemed all right. I let it accumulate to the water temperature in a vase with treated water, and then I let it go. I was about to move it to a much larger twenty gallon tank todday until I noticed little red bits of its floating around in the water, and the frontal fins and back fin look like it's shedding its skin, almost like a snake.

Water parameters are fine-- ammonia/nitrite/nitrate all 0 ppm.
Only just got the fish two days ago, so I haven't had a chance or need to change the water yet.
The only stuff I put in the water was a dechlorinator/heavy metal remover.
There's no other fish in the tank.
Like I said, it's a medium-sized vase.
I haven't added any fish since then.

Tank size: medium-sized vase.
pH: 6.8-7.0
ammonia: 0 ppm
nitrite: 0 ppm
nitrate:0 ppm
tank temp: room temperature

Please help. It's my mother's fish, not mine. Although I've kept fish before, I've never seen anything of this sort happen.

 

[WILDER]

What your tap nitrate reading as it's rare to have a reading of 0.
Any red edging to tail fins or red streaks in the fins.
Do you mean red bits that have come away from the fins.
Any signs of flicking and rubbing.
Peeling skin can also be bacterial aswell as bad water quality, parasites.