Platys,cycling,white spot,nitrites?

Question
I am a complete novice to fishkeeping,no knowledge whatsoever.
4 weeks back i rescued 3 platys from my neighbours who were leaving,they were going to flush them down the toilet.It was a rush job,i bought a 5lt tank and put them straight in.
I did not know anything about cycling then,but after being on a few fish forums i now know that was the wrong thing to do.I have a API master water test,tetra safestart,tetra aquasafe.I only bought the testing kit last monday,did not know of it until then.Have been testing daily,all readings are 0,except nitrite,which goes off the scale.Have been doing 2 50% water changes everyday,and putting all required solutions in.But nitrites not going down.
Now one of the fish as white spots,noticed yesterday.Went to aquarium shop,and he sold me some medicine for it.Put it in tank when i got home today and took the carbon out of the filter.
But in order for the meds to work,you are not to do any water changes,but you need to do water changes to get the nitrites down.I do not know where i stand and what to do next,the fish with white spot,now seems to have more.Any advice please.

PS another local aquarium is giving me some mature filter media for good bacteria,but not till Sunday though.

Answer
Hi Natalie,
Do not worry about the nitrates now.  The main thing is that your ammonia is O.  Put in the medicin and cure your fish.  Do not make water changes,and remove the carbon.  If you have a heater raise the temperature to 80 degrees while treating them. Then you can lower it to 78 when they are better.  They should be cured by Sunday.  If not wait till they are cured before putting the mature filter media in.
When the fish are better, do a water change,(25%)  Never make 50% water changes twice a day, this could kill your fish.  In a five gallon tank, remove 15-20% water a week.      The mature filter media should be okay.  Remember to add good water conditioner with very water change.
If you need to know more, don't hesitate to write me...and congrats for saving these little fish from a sure death.  Wish there were more people like you.
Hope this helps
Lynda