you definitely have a sick fish. i think the best treatment for sick goldfish is what is called the salt treatment. make sure the water is clean, aerated and use dechlorinater. keep the fish in 1% salt solution as described on the package for healthy fish. if you have a sick fish you can increase that to 3x the recommended for a few weeks until the fish recovers. this amount will damage live plants so don't do it in a planted aquarium. but aquarium or pond salt from a pet storeÂdon't use table salt as it usually contains iodine. kosher sea salt is ok, but will cost you 10 times what pond salt will. it is very cheap and as effective as most medications. it will contribute to the overall health of the fish so you should use even if the fish are healthy to increase thier slime coat and protect their gills from nitrate damage. i try not to use medications because they often harm bacteria cultures and will cost more than the goldfish. i use salt constantly and have never had a sick fish that did not come to me sick.

water changes are usually beneficial as long as you treat the water, keep the temperature constant and don't stress the fish when you do it.

good luck.