My fish have torn fins.

I have yet to check the perms, I wanted the fish to calm down and settle before I check. It's been 2 days since the tank was moved. I did not clean the filter, I left it alone and I put the biowheel into the cooler the keep it from drying out.

My tap water doesn't contain chlorine or other chemicals like the old tap I used to use at my dad's a yr ago.

I have 5 loaches, 2 SA bumble bee cats and two small plecos, besides the 4 cories... and they flip when I do a 20% weekly water change. My ram hides and so do the neons.
 
It's a pretty good idea to do a water change now, then. You shouldn't have any ammonia.

My rams are pretty unaffected by my performing a water change. They just move away from where the water is coming in, but not in a panicked hurry.
 
Clean water goes a long way in healing torn fins and preventing secondary infections. As mentioned, showing ammonia is never good and may be a side effect from the change over. Water change, water change, water change...no need to worry about stressing any fish. I also don't see why you would add any salt at this point, especially water softening salt...
 
That ammonia says to me "Cycle, coming up!" so I'd check your perms daily until it goes away. Besides that and water changes there isn't much you can do.
 
You can not do too many water changes. Discus folks do 100% water changes daily and have perfectly cycled tanks....the bacteria is in your substrate and on your surfaces and in your filter. You don't remove them by doing water changes. Water changes are the safest thing in the world to do. You don't have to do a gravel vac...just siphon off the top and refill slowly. They probably won't even know you did it. If you do add salt be careful how much you add with the loaches in there.
 
Also, some of the first signs of ammonia toxicity are damaged and frayed fins. Anytime you move a tank and do all that shaking up you are bound to have a mini cycle. It won't be that bad...but another reason to do frequent water changes!
 
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