I got the idea from a short documentary I watched a few months ago. The writing style and characters are all totally my own. I know it sounds silly, but is this OK?
Seems fine to me. Ideas have to come from someplace, whether personal experience, imagination or an accumulation/distillation of the ideas of others. You put your personal stamp on it with your style and characters. I don't consider myself a writer --I've only tried to write one story ever, so take this for what it's worth. Good luck with it.