She doesn't have to aim it, that's true, but she also CAN'T aim it. It automatically splits the damage among everybody in range, no prioritization to champs. She has to position well to focus the damage on a single target during any point in the game. Her waveclear is garbage. If she cleared out all of your minions and you stayed in range to get Q'd, you deserve to take that damage.
You should have punished her short AA range when she came in to clear those minions so that she has to give up her health to get farm. Good trades lead to a health advantage, and a health advantage leads to forcing an early back or getting a chance to all-in. It's like Laning 101, man.