As an English major and only and English Major,
school is the proper term for a group of fish.
Herd generally refers to mammals only. For instance, you never hear of a herd of birds, it is a flock.
However, as an endearing term for one's own school of fish in American English, herd will work just fine.
I take issue with individual koi being referred to as a "piece." I find that much more demeaning and inaccurate than herd. Look up piece in the dictionary. It ain't a fish.
