Hi there.
We'll do our best to help you figure this out but I think there's a little bit more info needed to figure out the source of the possible bacterial infection.
Firstly, are you familiar with the nitrification cycle and its end product, nitrAtes? As you may have read, nitrates cannot be filtered out, nor can they evaporate. The only practical way to remove nitrAtes from the tankwater is to perform waterchanges as dictated by the results on nitrAte test kits. NitrAtes have a toxicity level at or around 40-50ppm and anything higher than that for too long can cause serious health problems. It is best to keep them 40ppm or under. They may not appear right away, but if a high level of nitrAtes isn't eventually quelled, you can bet someone in the tank will feel the affects. Some sooner than others. Because you have not listed a result for a nitrAte test kit, I can only assume that you don't have the kit for it and don't know the level your tanks water is at. Without knowing what the nitrate level is at, you can't know how much water you should be changing
weekly. This I fear may be the reason why you are seeing problems starting in your tank.
In a high nitrAte setting goldfish immune systems are compromised and this allows all types of bacteria, fungus and parasites a good foot in the door for infiltration. This may be the reason why you saw a spot of fungus on one of them.
So, with this in mind, here's your best course of action so far:
If your pH out of the tap closely resembles the pH in your tank (within 1ppm) you should perform a 50% waterchange once a day for 3 days. In this time frame, you should go to the store and buy yourself a nitrAte test kit and test your tankwater. It would actually help to get the kit and test before you change some water but I think your fish need the water to be freshened up ASAP.
By the way, how many fish do you have in the tank and how big are they (each)?
How many gallons per hour is your filter rated at and do you keep it on full flow?
And how about the fuzzy spot, did you actually see it fall off???
Post back soon!