So we won a bunch of goldfish at our kids school carnival 3-4 years ago. Well we still have 1 left. We had to move him from a 20 gallon tank, to a 75 gallon tank. Because he is huge! His body shape is like a normal goldfish but much, much bigger! And his tail is just as big as his body but like a full, huge fancy tail. I can't find any pics on the net of any other goldfish that look like him/her. Just want to know what kind of goldfish him/ her is? He just keeps growing too! And has survived all the water problems we have had over the years.
Betta fish are a popular aquarium fish, they are durable and can have a large tail. However, I haven't seen anywhere that they can grow over three inches. One large pet fish is koi. They can grow very big. It seems unlikely that your school carnival would hand out koi, but you never know. I hope you don't have a koi, because they can get HUGE. Another popular aquarium fish is tetras. Looking around though, I don't see any big and/or big tailed ones. A black Skirt Tetra has a big tail but doesn't grow very big.
Other than that, I can't find anything else, although I'm no fish expert, everything here I found is on the internet. None of these fish quite match your descriptions. Well, good luck with your fish!