You don't really provide much information for anyone to locate a potential problem....but it sounds like ich. Ich is most noticeable in the fins.
I have had excellent success in treating goldfish and many tropicals with just salt. I make a concentrated salt solution so that when it's added to the tank it results in 1 tbs salt per gallon of water (1 tbs = 3 tsp). I add salt as a solution because it bothers me to watch goldfish go after salt crystals like they were food...even though it probably wouldn't hurt them. Anyway, I add one-third of this solution to the tank at a time and wait 6-8 hours between doses to allow fish to acclimate to the rising salt content. I run the tank at this salt concentration for 10 days. The worst thing I've had happen is some plants (in tropical tanks) get a little "aggrevated" but they recovered when the salt was removed. Salt will also control a number of other common goldfish parasites/pathogens...except flukes.
Continue with salt and water changes. Antibiotics might not be completely effective until potential parasits are under control.
If you do not see improvement then a fluke treatment might be necessary...especially if your fish was recently purchased. Body and gill flukes are common goldfish parasites and can stress goldfish resulting bacterial infections, ich, and other secondary problems.
Good luck.