First a new neon tetra, then a day later, our 2 year old betta :(

Hello all, yesterday one of our neon tetra's we introduced into the tank had died. We had just introduced it 2 days ago, and I noticed that it had turned a pale color in the morning. When I came home from school, I found it dead. I disposed of it, thinking it died from not getting acclimated to the tank.

Sadly, this morning, Johnny Bigmac the 2nd, our betta, was incredibly pale and looked like he had caught "ich" within the time I disposed of the neon tetra, and the time I was asleep. I told my dad to go to our LFS and ask him what had happened to our fish, and hopefully buy medicine for Johnny. When I came home, I found the medicine on the table, but Johnny was missing. I removed the cave, only to find Johnny's lifeless body there.

I feel terrible, but I wish to know why he died, and if there is anything to prevent this from happening in the future. Obviously I believe it is from "ich" but does can it really kill a fish without showing visual signs within 24 hours?

I also cleaned the tank after I added the new fish, and rinsed off the filter, because it was blocking the bio-wheel from moving.

Thanks for the replies, I feel terrible, as I appear to have made plenty of mistakes as a beginner fish keeper. Since our family considers Johnny a part of the family, I think we'll give him a proper burial, for good times sake.

EDIT: I bought the neon tetras from petsmart, they have given us good healthy fish before, but I guess we had a bad one

20 Gallon tank, it was stocked with 4 platies, and a betta. Then we introduced 5 neon tetras and a pleco (can't remember the breed, the sign said this one grew up to 4 inches compared to the 20 inches of normal ones). The tank runs on a penguin filter, which had one filter in it's cartridge, which was rinsed the day before the neon tetra died.
The tank is about 2 months old, and was cycled by placing our betta in the tank (previously in a bowl).
I do not have a test kit that gives readings, but I use an API one that uses color. When I cleaned the water, the ammonia levels were in check.
I do about a 15-20% water change weekly.
We left the tetras in the bag in the water for about 5 minutes, then added some of the water for another 5 minutes, then we let them loose.
All we add is food.

Thanks for the replies.

To prevent other fish from getting ich, I added a chemical that included malachite green called QuICK Cure, and added the amount that it recommended for neon tetras. However, later, my mom added MORE to it without telling me. As soon as I heard I did a 15% water change with the water treatment chemical as always.

However, this morning I noticed Isabella, our red wag platy was constantly opening her mouth. I thought she might be suffocating so I looked up some info, and it appeared true. In hopes of adding more oxygen to the tank I lowered the water level by about an inch. This afternoon however, I came home from cross country to find her dead. Should I get an air pump? Should I transfer my fish to a friends tank for the time being?

Thanks for the replies, hopefully this mistake will allow me to become a better fish keeper to prevent this from happening in the future.

So, could our betta have died from ammonia poisoning? Is a common symptom turning white around the gills and then the rest of the body?

On the other hand, the platy that died did not change color, but was gasping for air.

To prevent more fish from dieing, should I do a water change? When I tested the water it appeared to have .25 ppm instead of the normal 0 from the ammonia testing kit.