Possible to Fix Eye Position on Head?

It is difficult to "fix" asymmetric eyes completely.  Craniofacial surgery is required.  This is performed by plastic surgeons specialized in craniofacial surgery and is usually reserved for children with severe problems of eye height difference.  They involve moving the bones of the eye around.

There are camouflage procedures that can be done to minimize the asymmetries.  These procedures are performed by plastic surgeons who take the time to notice and evaluate all your asymmetries, and come up with a highly individualized plan to maximize your beauty and symmetry.  Often they involve carefull planning, asymmetric browlifts, upper eyelid lifts, cheek augmentation with fillers or implants, etc, possibly involving the entire face.

Every patient is asymmetric if you look hard enough.  It is important to point this out to the patient before the surgery so they will not be disappointed when they are not symmetrical postoperatively.

Patients should never lose focus on what is important.  It is not important to be absolutely symmetric.  It is however important to make sure that plastic surgery makes the patient as beautiful as possible.

Asymmetry is the RULE of nature not the exception. Almost every feature in our body is asymmetric. From our ears, eyes, cheeks, smile, breasts, limbs even butt cheeks.  Correcting some asymmetric features are much simpler than others but in general asymmetry can be narrowed and minimized but never fully resolved.

When it comes to the eye sockets, the craniofacial surgery required to move those about is extremely specialized and complicated and requires sawing the skull and moving segments about and then fixing them with plates and screws. Such surgery is associated with prolonged recovery and complications and is reserved for reconstruction of significant facial trauma, facial cancer surgery or congenital deformities.