okay to begin with, your tank is not big enough for two Oscars so you should really only have the one. The only way you could confirm that your fish had parasites was to get the waste examined under a microscope. However, White Fish waste is sometimes an indication of an internal parasite. This cycle stuff does not instantly cycle tank, I want to make that absolutely clear. Many people are on the impression that it does and they just put all the fish in the tank together far too soon.
Cycle does work to a certain extent, but only if you add fish very gradually.I have only ever used on a very small community tank where it did work. Without going into complicated detail, I think that cycle actually works by introducing free swimming bacteria that consume Ammonia in the water, rather than adding bacteria to the filtration system. because you are adding it on a regular basis, the free swimming bacteria are consuming the Ammonia while the bacteria have time to grow in the filtration system. Sorry if you do understand this, you have to know little bit about how the biological filter works to really understand what I'm talking about.
anyway, what you have got to do is test your water for ammonia, nitrite and pH. How long has the tank been set up for? If you are going to continue having ammonia present, you could actually benefit from using something like prime, this will detoxify ammonia so the environment is a little safer to your fish.I would also suggest not vacuuming the gravel, you want to try and conserve as much bacteria as you can, Cleaning de Sand will actually remove some of the bacteria.
I would advise you to carry out a 25% water change every other day until your Ammonia and nitrite are zero. you will also need a nitrate test kit. It is very important that you start testing this, once you start seeing a nitrate reading, you will know that your bacteria are present in your biological filter. It will nitrate stays at zero all the time, there aren't any beneficial bacteria working properly.