Who hasn't heard of Backwater Gospel? That animations has been around for 12 years.
Nick already posted Opal so I can't think of any really emotional ones, Curve is a bit upsetting with the use of sound and the secondhand pain from seeing her horrifically friction burnt hands.
The Little Goat I wouldn't considered scary horror, but it has disturbing themes.
These aren't short but if you can sit through them, Skinamarink is kinda fucky, Lake Mungo is good if you're fine with documentary style quiet, sad movies, and Train to Busan is the saddest zombie movie ever imo.