This looks like a bacterial infection, most likely, not to belabor the obvious. Rarely a viral, but most likely bacterial. There are several kinds of bacteria that can present like this so I would go with a good broad spectrum antibiotic.
Considering the size of your tank and the dosing requirements of several antibiotics I can think of, and the fact that you need to rely on others to do this for you, I think Kanaplex would be a good choice.
Kanaplex is a broad spectrum antibiotic that is absorbed through the fish' skin, which is important, and it has a little scoop that will be the proper dose for that tank (level scoop per 5 gallons), and would be much easier than trying to divide and correctly dose Maracy and Maracyn 2, (another good combo of antibiotics), for that size tanks as the packets are premeasured for 10 a gallon hospital tank.
I would lower the temperature in the tank, slowly, to about 75 degrees to help slow down the spread of the infection. Columnaris takes off at temps above that, and while we can't know for sure at this point which specific pathogen is involved, this certainly could be Columnaris, which can present with redness at the mouth, and which is why Columnaris is sometimes called "mouth rot" by different individuals.
Any of the pathogens Cerianthus mentioned may be responsible, that's why a good broad spectrum or combo would be good.
Start with a big water change, removing in carbon from the filter. Dose the tank. Next day appx 24 hours later do another huge, (90% if possible) water change and dose again.
I would use Prime to help with traces of ammonia and/or nitrite, and make sure you remind your neighbor to keep the temperature of the repacement water matched with the tank water.
One could suggest that isoloating the sick fish from the others would be a priority, but I'm thinking the other fish have been exposed and I would go ahead and include them in the treatment plan.
I would do the water change and dosing for 10 days. I've done this successfully and have had excellent results, using Kanaplex, and in other cases the Maracyn/Maracyn 2 combo the same way.
If you can't find Kanaplex (kanamycin), trying to keep the workload issue as simple as possible for your friendly neighbor, I would get Binox if you could find it. (there's a little scoop in that as well, so dosing is easier).
Also, if none of the above are possible, then I would get Jungle Labs Fungus Clear, which is really for bacterial infections and does treat true fungus as well. I've used it successfully, still doing the daily WCs and dosing, (must do the huge WCs), and although it is a tablet for a 10 gallon, it is easy to score the tablet and break it precisely in half.
Jungle Labs also makes medicated fish food, called Jungle Labs Anti-Bacterial medicated food. I would get that and feed that exclusively, and lightly, so meds are getting inside the fish as well.
I hope this helps, though it's a shotgun approach to treating the fish. He may be very sick and too far along to help, but it's worth a try and I would go ahead and treat them all.
