they look like they're flying because there's no indication that we're seeing them through water
Looks a bit flat to me. And, like Jabber mentioned, fish look like flying. It's a nice, calming atmosphere though.
The shadows make them look like they're flying... Perhaps if they were further from the edges, or if there were reflections on the water above them, it'd look better. I like the colors and composition though.
I really like the colours in this, but I think the others are right about the shadows of the fish, it really makes them seem to be above the water. Adding some reflections over the top might help, or lessing the shadows of the fish maybe, but I wouldn't really know what to do to create a realistic effect without looking an overhead photo of fish for a reference first (to see how lighting and shadows would act in a case like this). Good luck in the challenge though! : )