I remember reading this story many years ago (at least ten).
A young girl (at least I think so), discovers that she has magic by throwing something. However, magic is restricted (or maybe even forbidden) and she must now hide from all magicians in her city. I think the local Thieves Guild helps her, hoping to get their own pet magician.
Other recollections:
- It's low-fantasy, no elves or dragons
- I think there was a lot of homophobia in the setting
- I seem to recall that she can't control her magic and is eventually caught/taken in by the magicians.
- I'm pretty sure it was a full-length novel. Possibly a novella.