Tetra with Red Gills in Uncycled Planted Aquarium

So here's the chiz,
I got 8 neon and 8 rummynose tetras in my new uncycled planted aquarium.
One of the 8 tetras has red gills on one side, while the others have slightly red gills which sort of look normal. I can't tell with the rummynose, but they're behaving like normal.
The neons are behaving normal except they hide more often, especially the red gilled one.
Just to be clear, I didn't intentionally get tetras for my uncycled tank. My dad owned a few aquariums a few years ago, and he doesn't believe in the whole "cycling biz" since he never cycled his tanks before but all his fish (except one) did fine. He owned flowerhorns, arwonas, plecos, goldfish ,etc.
I wanted to buy a few guppies to cycle the tank before adding fish, but without my knowledge my dad bought 16 tetras, and put them there. Now, that I'm trying to tell him there's an ammonia spike and I need to change the water. He says that if I do the fish could get stressed and die since the tank is only four days old. He says just let them be, It's natural for one or two to die at first.
What should I do?

I do use water conditioner, and I have 2 water sprites, a few amazons, java moss and some type of fern. The plants have been there for less than a week before my dad added the fish. I think I will start changing the water. I will purchase test kits soon. They're a bit harder to get here in the Philippines. Thanks

So, I just changed the water in my tank. The one that was doing the worst died while I was changing the water. One neon is missing, probably hiding. One neon is really stressed out and won't eat. The rest of the neons are doing fine, hiding more often, but fine. The rummynose tetras seem unaffected.

So the really stressed out neon died as well, and I think it was because of the water change because they both were sick then stressed by the water change. Therefore sick + stressed = die. Is there anything I can do to make the water change less stressful?