Dangerously high Nitrite levels in my freshwater tank! Help!?

Last month I bought a new 10 gallon tank. The goldfish died a week later; I now think it is because I used well water (treated by water softener) and also maybe because my husband forgot to put the carbon filter in the tank when we set it up. I have distilled water in tank now & nitrites are still at 3! Alkalinity is also at 40, but everything else seems fine. I put the carbon filter in this morning. Any ideas as to whether the current problem is from not using the carbon filter or is something else going on here? THANKS!