Ick is likely to kill some of your fish. The ones that survive will likely become somewhat resistant to it.
Since your tank is newly cycled I suggest you use the high temp method that Aquarist48 suggest. It is "tried and true".
The "salt-grain-like" cysts that are visible in the fish are untreatable. Ick is a protozoan parasite, that has a complex life cycle with three stages. When the cysts disappear it doesn't mean the problem is over, it means that it entered the first stage, where this organism drops down and attaches to whatever surface it finds (plants,
driftwood, substrate); from there it will turn into a free-swimming phase, looking for a host to attach to.
If you feel up to the task, besides increasing water temp and levels of dissolved oxygen, consider the following: Thorough cleaning of aquarium walls, plants, decor followed by huge substrate vacuum, media filter gently rinsed in treated tap water, and as huge as you can every-other-day water changes (safer if you can mimic the tank's water parameters the best you can as far as temperature and pH).
I wouldn't use aquarium salt in new tank since beneficial bacterias that sustain the nitrogen cycle differs if salt is present or not in the water column, although I don't know at what concentration level (-ppt?) this is critical. I could be wrong here.
Pepe
Santo Domingo