The pixies wings are more than damages: this is the equivalent of breaking someone’s legs by tearing tendons and shattering bones. If the pixie does not get proper medical treatment, either mundane or magical, her wings will not heal right and she’ll never be able to fly again.

The closest thing to a doctor is the ship’s chef. He also doubles as the ship’s chaplain and has training from the church of Gusstha covers basic injuries one might receive while operating a ship, but you’re pretty certain that he’d never receive training on how to fix a pixie’s wings.