Hi Lynz781
I'm sorry to hear about your cory. It has finrot, which is a bacterial infection that is not at all unusual in corys that have recently been shipped from one place to another. There is still a good chance you can save it.
Right now I have 4 wild caught C. trilineatus that I bought last week that I am treating for the same problem. They are still hanging on and perhaps improving. I wouldn't have bought them, since I knew they were sick, but they were the biggest 3 line corys I ever saw.
First, if you can isolate him for treatment, do so. In fact, move all the ones you just bought. If not, give your tank a good cleaning and bottom vacuuming. Change about half the water. Add MelaFix to the new water.
Then give your sick fish salt baths. I do this by taking some water from the tank and mixing in salt at the rate of 1 tsp. per 2 cups of tank water. Put your sick cory in it for 20 minutes or so. At first, it might not tolerate that long, so be prepared to remove it sooner if it rolls over. It will revive as soon as it goes back into the fresh water. Repeat this for up to 6 times a day until it is cured.
The concentrated salt bath will act much as when you put peroxide on a wound. It sort of eats away at the bad tissue and active bacteria. MelaFix is a mild antibacterial and will slow it's regrowth.
It will take a little luck, but it's an old fashioned treatment that still works.
You could also try using an antibiotic, but if you can't isolate your fish that would mean treating your entire tank.
Please let me know how things turn out.