There are hundreds of different "diseases and problems" goldfish get. However, if you're not seeing any other symptoms, just the finrot, don't worry about looking for an illness that's not there. Right now, we want to concentrate on the finrot. Which is probably a water quality issue.
For now, if you can't test your water, put everyone back in the tank and perform a 50% water change with dechlorinated tap water. Heat the tank (SLOWLY) up to 78 degrees. This you'll want to be extremely careful about. No more than 4 degrees per 12 hours. So if you're at 70 now, turn your heater up to 72, wait 6 hours, then 74, wait 6 hours, then 76, wait 6 hours, then 78. You don't want to shock the fish.
Finally, add some aquarium salt (NOT table salt)- about two tablespoons. If you have Prime, add some of that as well.
The heat and salt help fish heal, and since you're probably having a water quality issue, the 50% water change will help that.
How many fish are we talking about here? What sort of filter do you have on the tank? And how often are you vacuuming the gravel and doing water changes?