The ammonia reading you are getting from the tap is probably from the chloramine used to treat the water by the city. Chloramine is a compound chemical made by bonding chlorine and ammonia. Treat the tap water with dechlorinator, stir it well, then test it. See if the level changes. If it reads just under 0.25, that is fine your tank's bacteria will grow to compensate. If it reads between 0.25 and 0.5, do a 50% water change. If it gets up to 1.0, then do a 75% water change. You need to trust that you removed 50% or 75% of the ammonia during the water change to keep the level low.
I know this can be hard, and that sometimes things look impossible. But in the end, your tank will develop good bacteria to fight the ammonia in your tap, and right now you just need to find a place where your fish can pull through while that happens. An ammonia remover such as AmQuel Plus would probably be best now, just for the tap water coming in. You do need some ammonia right now so your developing bacteria have something to feed on.
Until you can get an ammonia remover and your bacteria is established, there is not much you can do. If you have plants and a good filter then you are doing pretty much everything you can. Extra aeration during this time of stress on your fish is ideal, high oxygen levels will help the fish survive ammonia levels. I know it is a lot of work, but try to keep ammonia below .5 until you can get some AmQuel Plus. It is sold at PetSmart. AmQuel Plus looks really good to me:
AmQuel Plus is nontoxic
AmQuel Plus removes nitrite.
AmQuel Plus removes all forms of ammonia.
AmQuel Plus removes nitrate.
AmQuel Plus does not affect the pH.
AmQuel Plus does not interfere with the beneficial nitrifying bacteria or their food sources.
I hope this helped if you are having issues with cycling a tank with high ammonia levels.
Here is a picture of my young ryukin that has recently grown really large. I feed her Hikari Wheat Germ, and she loves it and it is great for her digestion. I am sorry this photo is a little blurry. The water looks kind of nasty in this picture, and you cannot see her pretty metallic scales. I guess I will just have to take another photo later.
