Okay its more likly to be Bacteria than Fungus, as like Orion Girl said, True Fungus is very uncommon. Your fish tank is full of bacteria, some friendly some not, normaly your fish's immune system deals with the bad stuff without a problem, but if your fish's immune sysem has been weakened, like is probably the case with you where your fish have ich, it makes them prone to bacterial infections, also new tank syndrome which I recently went through when a new tank is 'settling in' can cause bactrial numbers to get out of control. It sounds like your fish are stressed from the ich and the move to a new home and this has caused the fins to shred and a bactrial infection to happen. Your main concern is treating the ich in the way you are. Most fish will be able to get over a bactial infection themselves with time and the salt will help as well just keep an eye on your water conditions.
Here are some pics to give you a better idea. The middle one is a bacterial infection and the other two are fungus, as you can see there is a big difference!
