It doesn't sound like you are doing anything wrong.
An aquarium takes time to cycle (develop the nitrogen cycle).
If your fish appear to be ill, treating them with medication may be necessary.
Continue doing partial water changes, I'd recommend 15% daily until your aquarium is fully cycled.
You will be able to tell when the cycle is complete when you have a 0ppm nitr
ite reading and a 0ppm ammonia reading.
Please read this sticky note at this link for a better explanation of
the aquarium cycle/nitrogen cycle.
Once your aquarium is cycled much care must be taken not to clean away the good bacteria. Your filter should have come with some sort of bio media for the good bacteria to live in.
This media should not be cleaned.
If you have any questions, I'm hear to help.
If your not sure what the bio media inside your filter is, you can give me the make and model and I'll find it out for you.