The Turret behavior is mostly intended for top-down games. In a platformer, especially if you’re only shooting left and right and there are no flying enemies, you usually don’t need it.
My advice: don’t use the Turret behavior. Pick the nearest enemy and spawn a bullet in its direction.
If you really want to use the Turret behavior, create an invisible sprite just for it. This way, you can combine the character and the gun in one sprite and mirror them easily.
Also, use hierarchy instead of the Pin behavior — child objects in a hierarchy will automatically mirror when the parent sprite is mirrored.