Did ya'll look in her mouth once a member found a piece of a stick under the tongue of her goose it had somehow got lodged in there. I know grasping at straws but might as well check out every possibility
What did the vet say about what you describe she is doing with moving her head around like it's bothering her?
@casportpony can answer about the safe guard.
@casportpony What about this moving her head around like something is bothering her? could that be a sign of gape worm? Surely if she had something stuck in there she wouldn't be able to eat like OP says she does?
Gape worms are in the trachea can she honk? when my rooster had gape worms he lost him voice completely. I'd worm her with safe guard for goats its a liquid or safe Guard horse wormer paste.
Is she eating and pooping normal?
@casportpony can give you dosages.