Hi there,
If one of your fish has visible ick, then your aquarium is already infested with ick, which means removing the fish will not remove the ick from your aquarium. My preferred method for ridding ick is a product called Ick Attack by Kordon. It is herbal and gentle on the fish and can be used safely with plants, inverts etc. It is brownish in color and may temporarily stain corals. Along with the Ick Attack turn your heat up as much as you can safely go with your occupants. Kordon Ick Attack takes a little time to work, its not overnight, patience required. You can use it twice a day when you've got the swarmers.
With that do a 25% water change with vacume every day.
I would use Prime by Seachem, two drops per gallon daily, and with your water changes at two drops per gallon, for every day that you either do not test your water or that your parameters read over zero ammonia or nitrite. Prime will detox your water and protect your fish. Ick tends to be a sign that water parameters are not safe so do be testing your water. A product like Stability by Seachem has positive microbes that can keep your cycle and water healthier.
You can separate and treat a fish still, if it seems it needs it and that will likely work faster than having the fish in the aquarium, but you will still need to treat your tank. I have never had an ick outbreak that I couldn't cure with Kordon Ick Attack. Be watchful for icks cousin though, Velvet, which is much more stubborn and requires immediate attention.
Good luck!