Hi chris-geiger and welcome to TFF!
Ok, from what it looks like, your fish shop has given you the wrong information and hasn't given you the correct information to get your tank started. We see many cases of this every week, so we have it down to a science.
Read the links provided above, and they will explain what is actually going on in your tank (bet you thought fishkeeping was about fish and not about bacteria

.) There are a few things you will need to be successful: a liquid reagent based test kit (we like and use the API Freshwater Master Test kit. They are around $20 on Ebay) and a gravel vacuum for cleaning your gravel and doing waterchanges. Those 2 items are essential in that the test kit lets you monitor your progress with your cycle, and the gravel vacuum lets you suck out any uneaten food and fish poop.
I'm sorry to hear that your fish are ill. May I ask what kind of fish you have? Whitespot is a parasite with a real long name, but usually referred to as ich or ick. Ich is treatable, but it has a few rules. While the spots (cysts) are still on the fish, the cysts cannot be treated. You have to catch it in it's larval stage so that they aren't protected by their hard shells. Luckily for us, there are many treatments out there. They range from a blue green chemical you add to the water, tablets that are dissolved in the water or they can be treated as simply as adding a measure of aquarium salt and turning your tank's heater up to 29C (84F.) Whichever treatment you choose, make sure you follow the instructions.
What size is your tank? What kind of filter do you have? These things will help us in assisting you further.
Hope that helps!