Hi Fillyfolly,
Please calm down and don't panick over salt and treatments. Could you please post your water parameters? Please be sure you are using liquid test kits by API to have accurate results. Test strips are inaccurate unfortunately and therefore, entirely unreliable.
Secondly, I would like to know your tank size and other fish in it. What strain is this goldfish? Is it a fantail? Pearlscale? Comet? Tank size really matters as the overall space influences the rapid deterioration of the water quality contributed by the massive production of wastes by goldfish. There are also plenty of fish that see their long trailing fins as a nipping temptation. If I were you, please feed your goldfish once a day only within 2-3 minutes and fast a day per week to help you keep your water quality in better control.
As far as guidelines are concerned, when you consider common goldfish, comets, wakins, jikins or shubunkins, make it 20g per fish to pave space as these ones truly grow monstrous to 12-18 inches. Fancy goldfish such as orandas, ryukins, black moors and many others, on the other hand, should be permitted at least 10-15g per fish.
In cases involving finrot, water changes are your main defense. Finrot is caused either by bacterial infections or rapid deterioration of water quality. Both cases can be rectified by water changes. Could you please post your filtration capacity and tank maintenance regimen?
Salt is not the answer to your problem. Salt has its limits in its scope and can only do much for instance, ich and nitrite intoxication, neither of which are involved in your case as it seems to me. Avoid the use of salt as it is totally unnecessary and useless in your case.
Without the needed information as indicated by my questions above, I cannot proceed to further advisory with very vague details. Please answer as much as you can so we may be able to prevent the situation from worsening in time.