I was just looking and saw this thread... I was heading to bed but just had to post a comment to help.
Ammonia appears first in the tank and is a by product of the fish pooing and peeing, and also the decaying of uneaten food or other debris. After a while a beneficial bacteria that loves ammonia begins to flourish in your tank and starts to break it down, this is when you start to see ammoina levels at 0.
Nitrites appear in the tank once ammonia is being broken down.
After a while, a beneficial bacteria that loves nitrites will be in your tank in sufficient quantities to break down nitrites which will cause the levels of nitrites to go to 0.
The process of breaking down nitrites then produces nitrates which are not as dangerous as the other two toxic by-products, but still must be monitored and removed either by water changes or by having plants that use nitrates as fertilizer, basically.
While the process is going on it is very important to do big water changes as frequently as needed to keep the ammonia and nitrites at 0 or as close to that as possible, and then when nitrates are there you need to keep them at or below 20.
Water changes do not stop the cycling process. In fact they are vital to protect your fish. You need to do big water changes, as much as needed to keep the ammonia and nitrites at undetectable levels.
It will help Skippy if you do daily water changes, with temperature matched water that has been conditioned to remove chlorine and chloramines. Prime is excellent and helps with detoxifying ammonia and nitrites for about 24 hours, giving you time to do the needed water changes to keep your ammonia and nitrites at 0.
10% every other day is not nearly enough. I would do at least 50% once a week since the tank is not really large enough, and maybe even twice a week until you can get him a bigger tank.
As soon as possible you need to get the API Master kit so you can test ammonnia, nitrites, and nitrates, ph.
I hope this helps. Really, Skippy needs a bigger tank and sparkling clean water. The water changes are the one thing you can do for him right now that will work wonders in helping him get well.... and in keeping him from getting sick again. If you can't get a bigger tank or rehome him then you really have to keep his water pristine by doing frequent, big water changes.
Monitoring the water parameters with the liquid test kit and then doing the needed water changes will help him tremendously.
Best wishes for Skippy's speedy recovery. Keep posting here on AC, the folks here truly want to help, and you can learn so much by looking through the forums and reading other threads. I've learned so much and have been helped so much by others here on AC. Keep up the good work for your buddy.