IS MY BLACK NEON TETRA SICK?

ok, i got a tetra for my birthday in a ten gallon tank i let the filter run for 24 hrs because that is what the person at the store said to do! but a couple of days later my fish got white spots on them! my friend said that they were sick because i didnt let the filter run long enough. then she said that i could buy stuff to make them better. can anybody tell me what is going on and if they are sick where i can buy these chemicals! PLZ ANSWER IMEDIATELY