Can I ask a few questions?
How big is the tank?
How did you set it up - did you add ammonia for several weeks before getting fish, or just set it up and put fish in?
Are you using strip testers or liquid ones?
You say you have fantails, bettas and a neon. Are the fantails fancy goldfish? How many bettas do you have? And how many neons?
Firstly the testers - strip ones are notoriously inaccurate. If you are using them you may well have ammonia and/or nitrite even though they show zero. The red marks could well be ammonia burns.
The white spots - do they look like the fish have been sprinkles with salt? That's whitespot, a parasite that often infects stressed fish. They could be stressed from having poor water conditons, and inappropriate tank mates. There are several makes of whitespot treatment on the market.
If you have fancy gold fish, they are cold water fish, while bettas and neons are tropical. The fantails will be stressed if the water is too warm; the tropical fish will be stressed of it is too cold.
Goldfish also need much bigger tanks thatn people realise - at least 20 gallons for just one fish, which is why I asked how big your tank is.
Bettas should not be kept together except for a group of females. Males should not be kept together or with females. If you have more than one male, or a mix of male and females this will stress them.
And it sounds as though you have one neon - or have I misunderstood? Neons are shoaling fish and will be stressed unless you have a group of them. They also do badly in new tanks, even where there is no ammonia or nitrite.
I wouls start doing daily water changes, they often help fish and are vital if you did not cycle the tank with ammonia before getting fish.
If you are using strips to test the water, you need to get a liquid reagent kit. You could also get the ammonia and nitrite levels checked at a shop - but get them to tell you the numbers. Anything other than zero is bad.