With a new race comes a new backstory as canon Fluttershy's backstory won't work with a unicorn. So instead, I have this.

Fluttershy was often bullied when she was younger, having no cutie mark at the time and generally being soft-spoken and shy. After a long while, she eventually got fed up with the bulling and ran into a forest. She passed out in a cave and when she awoke, she was surrounded by curious animals. She quickly befriended the animals and gained her cutie mark after the Sonic Rainboom happened and she had to calm them all down before eventually the animals guided her to an old run-down cottage near Ponyville, which she fixed up with the help of the animals and began living there.
She originally befriended Rainbow Dash first after she crash landed nearby after trying to preform the Sonic Rainboom again and Fluttershy nursed her back to health.