Mouth rot is bacteria-related, not fungus-related. It's very rare for saprolegnia to ever establish themselves unless the fish was left with untreated wounds and fungus is more characterized by creamy cotton appearance.
What are your water parameters (including pH)?
Do you have access to either kanamycin or tetracycline (not that I am suggesting to use either once you have them)?
Quarantine is definitely a good move. I'd add a teaspoon of table salt (without yellow prussiate included) per gallon every 12 hours. Stop once you've totaled at least two teaspoons per gallon in 24 hours. If you need to do a water change, be sure to redose salt per the water volume replaced. If you have to replace 5 gallons, dose back 10 teaspoons of salt. Whether it has iodine or not, it's not the issue. Just watch out for yellow prussiate.
