The fish died most likely due to ammonia poisoning, since you have a undersized tank without doing nitrogen cycle first.
After the fish dead, there is no immune system to stop fungus growing on the dead fish. Sometimes you will find a piece of left over fish food quickly grow fungus all over it within hours. It is the same concept here. Dead fish grow fungus doesn't mean the fish died because of fungus, it grew after the fish died.
The #1 ich/ick symptom would be white spots on the body, and the fish would "flash" to rub itself against objects because it is very itch.
If you show us a photo of your fish, we might be able to tell if it is ich or not, but you also need to know that ich doesn't kill fish that fast.
I strongly recommend you not to be paranoid over diseases.  Your number one concern should be getting the ammonia down.
For new fish tanks, I always recommend to use SeaChem Prime as water conditioner due to its ability to detoxify ammonia for up to 48 hours.
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