so the bacteria living mostly in your filter, but also on all the surfaces inside your tank, help to process the ammonia and nitrites. your fish are constantly producing ammonia which the beneficial bacteria will feed on. this bacteria, once established, will only handle the amount of waste your fish are producing. any additional sources of ammonia (uneaten food, decomposing fish) will cause an overload and you will likely see some nitrites and ammonia until your bacteria colony can catch up.
if you lose fish for some reason, some of your bacteria will die off because the remaining fish will not produce enough ammonia to support them.
when you add new fish, you are increasing the ammonia and your bacteria will again need some time to catch up.
i think what happened in your case is you had some fish loss, waited for a time (in this time your bacteria colony shrunk), and then added new fish (which overloaded your bacteria colony and resulted in readings for ammonia and nitrites. your new additions, the cat fish, were stressed with their change in home, and were also subjected to low levels of ammonia and nitrites. being scaleless and under additional stress from moving, they were more susceptible to the spike in ammonia and nitrites, and developed the trouble with their fins, while the established fish showed no signs/
to correct this, you can consider treating with meds, but should also do water changes to keep your ammonia at .25 max for now, until it gets back to zero....nitrites, zero as well. anything other than zero means your bacteria colony is overwhelmed. it shouldnt take long, as you only need to let your bacteria catch up.
i do not diasagree with bradberry, that water quality is very often the culprit.