For me the school book short story that grabbed me was The Smallest Dragonboy by Anne McCaffrey. Not super scary, just sticky.

Tsunami survivor realizes a part of him died with his friend that day. Messed me up. Don't remember the name

My senior year in high school, my English teacher started the year by having us turn in a list of all of the books we had read. My list was much longer than most of my classmates. He then assigned us books to read and report on based on some criteria (hypothesis: books that would make us miserable). I got assigned two existentialist plays, "Waiting for Godot" and "No Exit." I think those plays did permanent damage to my psyche.

(Sidenote: a classmate who didn't read very much got assigned Virginia Wolff. She thought it very unfair that I only had to rea d couple of plays.)

• "Gentlemen, your verdict" by Michael Bruce - trolley problem on a submarine (attention: weird vertical formatting)
• "Just Lather, That's All" by Hernando Téllez" - a barber during a civil war

The second one actually gave me half of a mental breakdown, but not because it was too violent for me.
One analysis that I read made the exact opposite conclusion that I made, and it showed me this: in the subject of English, two diametrically opposed points can both be equally correct! Nothing is fixed! Reality is mutable!

Also The Lottery, The Veldt, Harrison Bergeron (which others have already mentioned)

The Tell Tale Heart.

Though it did spark a lifetime interest in video games featuring necromantic main characters.

Alan and Naomi by Myron Levoy

It's a novel, but not a very long one.

Harrison Bergeron

The egg by Andy Weir

Not in english, but we read Anne Frank's Diary in grade 8, Andorra by Max Frisch in grade 9 or 10.

But the most disturbing was "Der Sandmann" in grade 11 and "Der gelbe Vogel" (originally "Alan and Naomi") in grade 9.

Zapped while zipping...