First off, Mike, don't cry. You aren't the first person to have this happen, and you won't be the last. The good news is that you are in the right place.
Second off, let's tell you what the nitrogen cycle is.
Fish produce ammonia, as part of their respiration, and in other bodily waste. In the wild, this ammonia would just be washed away down stream, but obviously in an enclosed aquarium, that doesn't happen. It poisons the fish.
So, the aquarium grows a biological filter of bacteria, not just in the mechanical filter, but on other surfaces too. Plants also help remove ammonia. The bacteria feed on ammonia, and produce nitrite. This is also poisonous, so there's another bunch of bacteria that eat the nitrite and convert it to nitrate. We remove most of the nitrate in our regular water changes, although plants also help with this too. This is the nitrogen cycle.
By "cycling", we mean growing those two colonies of bacteria, such that the test results will return 0ppm ammonia and 0ppm nitrite, consistently.
The bacteria won't grow without a food source (ie ammonia) so just running the tank empty for a few days basically does nothing. There is no food, therefore there is no bacteria.
Now that you have fish in the tank, there is a food source, so the bacterial colonies are growing - slowly. In the meantime, you need to keep changing the water manually, to keep the ammonia levels safe. The trick is to change as little as possible water to give the bacteria enough food to grow, but without harming the fish.
TwoTankAmin has written an excellent pair of articles which explain in a bit more detail the science behind it, and a detailed guide of exactly how to work out how much water to change, and how often. Obviously, as the bacterial colonies grow, they process more of the ammonia, so you need to do less work. You can find these pinned at the top of this section of the forum.
In order to do so, you need a reasonably accurate test kit, and as I said previously, I don't believe that paper strips cut the mustard. I strongly recommend getting a liquid test kit, P@H sell them, as do Maidenhead Aquatics, as do every independent LFS, as do Amazon and Ebay. Many people use the API kit (I don't but that's another story!), it is perfectly accurate enough for your situation.
The eye issues are symptomatic of poor water quality, and it does seem as though ammonia is your problem, so you need to get something to test ammonia soon, so you can start a proper water change regime to help your remaining fish.
Ask any questions you want, the chances are that you won't be the first to ask them, and that you won't be the last. The only silly question is the one you don't ask.