Fin rot again? Or bullying?

[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 tear on his fin that was not there before. 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?
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?

 

[Fishperson]

my tank is a 20 high, i do 5-10 gallon wcs every weekend, but i havent vacuumed the gravel yet, or changed the filter pad.

 

[Fishperson]

The one with that is affected is at the bottom of the tank, just hovering above the gravel. Something is definitely wrong with him. His nose is the palest of all of them. All other fish are fine.

 

[shellieca]

It doesn't sound as if you're QTing the new fish? It is possible the new fish are bringing in an illness. Can you post a pic?

 

[Fishperson]

Well I have always thought that QTing was an unnecessary step, so I didn't do it. And I don't have any other cycled tanks. The bacteria that cause fin rot are always in the water, but they only affect a fish if the fishes immune system is weakened.