How clean are you keeping your tank? The chances of a healthy fish in pure water conditions being infected by a pathogen or virus or anything else like this is very remote. So, even if you didn't quarantine this new fish, a healthy fish isn't at risk.
If your tank gets lots of large, regular water changes, then you have nothing to worry about. If, you're inconsistent with your tank care, then your fish may pick up something from a fish from the local pet store.
I'll give you a tip on tank keeping. Change half the tank water a couple of times a week if your tank is less than 30 gallons. If it's 30 gallons or larger, change half the tank water weekly. No excuses. Do this and you'll have no tank problems.
This white material is likely a form of fungus. Fungus isn't a problem for a healthy, well kept tank. Ramshorn snails and most livebearing fish will remove it.
"Fear not, my young apprentice. Just change the tank water."