(@N & F) Redness can also be bacterial. Much like an infected cut on human flesh takes on a localised redness. I think there are some blood disorders that will cause skin redness but like you say these can sometimes be linked with ammonia.
The picture posted looks exactly like "cotton wool" mouth fungus, which isn't a fungus. That's what I would aim at. It doesn't have to be your water quality or tank cleanliness. (Most people get defensive over such issues, there really is no need) we all love our water just as much as the fish, at least the people on this page must be keen on water. It's good to know water but. . .
Many factors can cause this, stress of handling, abuse from tank mates, water change (tank moving etc) simply catching the fish is enough.
It is treatable, many products available.
Apart from that, hope your fish are well