Wounds on fish rarely show up as white. It sounds as though your fish most likely has one of two diseases. The first one is body fungus, which is relatively common in goldfish. Stress is usually what causes them to break out in the fungus (such as bringing a new fish home, and putting it in a new enviroment). Body Fungus is relatively easy to treat with most commercial fish medications. A good one to try for this particular disease would be MelaFix.
Another possible illness could be Velvet disease, which presents with the same symptoms as fungus; white powder/cotton growth on the fish. To treat velvet, add aquarium salt to the tank (two tablespoons per 5 gallons of water) and treat with a medication called Copper Sulphate. This should help clear things up.
As always, do a 25% water change before and after treating the fish, and remove all carbon from your filter before starting the medication.
Hope this helps!
I am NOT, nor do I claim to be, a Veterinarian.
Always check with your vet for any symptoms your pet exhibits.
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