Hi sugamom
The most common disease to effect corys often starts with damage to fins, tails or barbels. It can be one of a number of bacterial infections. Some will progress quickly, and others slowly, but they are all treated the same way.
Bacterial infections are caused by ordinary bacteria that is in the tank. It's only when the fish have been exposed to some condition that puts stress on their immune systems that they become ill. These conditions can be overcrowding, aggressive tankmates, low oxygen content in the water, overfeeding (left over food spoiling) temperature fluctuations, elevated nitrites or other unusual conditions. The first thing to do is to identify and correct the problem.
Often, larger or more frequent water changes are needed.
I would suggest doing a good water change and bottom vacuuming to start with. Since you have large gravel, it's easy for uneaten food to get trapped between the pieces where the corys cannot reach them. You might want to add some MelaFix if you have it. Often that mild anti-bacterial will be all that is necessary to cure the fish.
If it doesn't show improvement in a day or two, or if they or any other fish in the tank show additional symptoms, I would recommend using an antibiotic or other preparation made to treat bacterial infections.
Good luck and please let me know how things turn out.