What is your water temp. now and do you have a heater?
When you prepare your water for the water change, please mix the declorinator at the amount to remove Chloramines too. Some times it is appx. twice the amount for Chlorine/ammonia alone, most of our water also has Chloramines in it. The chemicals in the water burn and damage the gills the fish use to breathe and they can't function as well as they should. And also heavy metals and other things in the water can harm them.
BTW for the aquarium salt, is pure salt, no iodine, no anti-caking agents, no additives. I use canning salt and sea salt, sometimes Kosher, for ingredients there will none other then salt.
Recommend 20% water change each day for 5 days with 1 Tablespoon of salt for 10 gallons, water
Then 20% water change each day for day 5-10 only 1 tsp for 10 gallons.
Goldfish do not require salt, but it helps them produce mucus / slime coat. I have used that and mine are in good condition.
You should turn your filter back on after the medication treatment is complete.
I hope your mother understands this takes some extra time but is best for the fish.
Make sure the water is the same temperature as the water they are in or a tiny bit warmer, 1 degree maybe 2, that is why you need a thermometer. Mix your aquarium salt into the water and dissolve the salt.
Moving and having a broken aquarium is stressful but all new rocks and filter is where the beneficial bacteria grow which help your fish have better water quality. So it is amazing the fish are still alive.
Water temperature is important to speed up the life cycle of Ick, It is recommended to raise the temperature 2-3 of degrees a day til you get to 78 degrees. Then after the is no longer seen for a few days, reduce the temp. 2-3 degrees a day to the recommended warmth for your fish Gold fish are "cold" water which really means cool water is good 72-74 degrees.
Also since you said you didn't originally treat the water in your tank, you should add additional declorinator to the tank water enough to treat for heavy metals, etc, in case you didn't use enough to neutralize that
The salt helps with goldfish to build a slime coat on their bodies, which helps keep them healthy and helps immunity.
The amount of salt is more when sick than during healthy times, 1 tablespoon when sick for 10 gal
, but only 1 teaspoon for 10 gallons if healthy. This is to be added during water changes. If your water evaporates and you are filling it back up, the same amount of salt stays in the water, and is not removed unless you take it out. Salt does not evaporate.