I just went through starting a new 10 gallon aquarium. I think I can help you some. The experts will need to jump in on what I am missing or, don't explain correctly. It appears you need help immediately, so I am going to post, regardless of the fact that I don't know what they do.
First off, do some water change, immediately. Your ammonia, nitrites and the resulting nitrates, are all way, way too high. I got a similar ammonia spike, and I ended up changing all the water in the aquarium but not in my filter to get the spike down to where it was not going to damage the fish's gills or kill my fish. I tested my water two and three times a day after that. I would also immediately get an airstone or bubble source to add oxygen to your water.
The fact that you have nitrates, means you have some bacteria that is active. I am sure there is not bacteria enough to handle the ammonia and nitrite load, however.
I suspect you are overfeeding or have another source of the above contaminates. Something is making all that ammonia and nitrites, and I don't think it is all coming from the fish.
Now, I had a cheap resin item in my aquarium... and I suspect it was the source for some of my ammonia and nitrates. I can't prove it... and I could be wrong, but when I removed it, the contaminates dropped. I rinsed it well, and scrubbed it too, but when I tipped it over after cleaning it thoroughly, and smelled the inside, it still reeked of chemicals... plastic chemicals. I will never use a product like it again. It is all natural for me from now on. I know it is better for the fish, the same as it would be better for us not to have to smell that awful odor.
Do not clean your filter in anything but used aquarium water. Doing so kills the bacteria. Unless your filter quits putting out water, I would not clean it until your aquarium starts cycling more and handling the ammonia and nitrites.
A load of nitrates also means you need to change some water. It is basically fertilizer, and you would not want to live in a room full of fertilizer either. It would not be healthy for you... as it is not healthy for your fish.
As to how much water to change... I would do one change of approximately 50%. Then test your water again. If it is still above .25 on either ammonia or nitrites, I would again remove and replace water until you get both back down to .25 or below. You need some ammonia and nitrites to get the bacteria count up.
If you have a friend with an aquarium that is cycling, and you know his tank is disease free, you could get some water from out of his filter, and add it into your filter. That will add more bacteria. REMEMBER... contact with fresh water by rinsing, will kill the bacteria. I believe it has to do more with temperatures than being fresh water. Also, chlorine and the newer chlorine substitute will kill bacteria. That is the purpose of it in our drinking water.
I kept the ammonia and nitrite level at or below .25 while starting up my 10 gallon. It took over three weeks, but it is now holding its own. <phew> I thought I was never going to quit hauling water. I was doing so EVERY DAY.
Gold Fin