rummynose has a big tear on his tail fin that was not there before

[Fishperson]

I have posted about this before, but I have a tank that I fishless cycled with ammonia on March 8. It has 7 bloodfin tetras and 5 rummynose tetras. My most recent test ( two days ago) got:
10 nitrate
0 nitrite
0 - .25 ammonia
7.6 ph
One of the rummynose has a big tear on his tail fin that was not there before. He did have a small tear on his tail fin when I first got him ( the 26th) but it has recently gotten worse. I left on a trip on the 27th, and when I got back a diferent ones fin was completely gone (tail fin). he eventually died, which I determined was from bullying by the bloodfins because they were hungry. Now what is wrong?
Is it fin rot or bullying?
Since I got back from the trip, I have not seen the bloodfins bullying anyone at all. I added 3 rummynose on the 26th, then one died and I added 3 more on the 1st. I plan to add 2 more to bring my total to seven next week, when my lfs gets more. So does this one have fin rot?
Is it bullying?
what should I do?
My tank is a 20 high and I do weekly wc of 5-10 gallons. I have not vacuumed the gravel yet or changed the filter pad. I do not quarantine my fish either, although i have access to a 10 gallon tank with a filter. I am pretty sure that both situations were fin rot, but what should I do to treat it?

 

[Fishanatic]

I wouldn't think it was because they were hungry, because if it was, they would have ate it. Was he ill and was he eating?
Also, what's the temperature in the tank?
I highly suggest quarantining fish before adding them to the stock. Also, he might have gotten bullied because he was sick.

 

[Fishperson]

What I was told was that since I did not feed any of the fish for 2 days (because I was on vacation) the bloodfins got frustrated and bullied the rummy nose, and he then got fin rot and died. How do I quarantine them if the qt tank is not cycled? The temp is and has been at 77

 

[Wiggles24]

Honestly IME "under feeding" fish CAN lead to some aggression, I know there are lots of fish keepers that skip at least one day a week in feeding but I have found daily feelings work well for limiting aggression

 

[Fishperson]

It does not seem to be getting worse, so I don't know what it is. Any other ideas?

 

[Fishperson]

I tested and the params are fine
7.6-7.8 ph
0 nitrite and 0 ammonia. He seems to be a bit better, but his fin is still torn. How long will it take to heal?