Is there a way to make my eyes look more symmetrical? (Photo)

Thank you for your question. I suggest that you move forward and consult with a board certified facial plastic surgeon. It is the next step in the process before you would move forward with LASIK or other options. Eyelid surgery can improve the symmetry of your eyes, and you can discuss your candidacy during your consultation. 
Best wishes,

The asymmetry has to do both with your right upper eyelid and right lower eyelid more droopy (eyelid ptosis and lower eyelid retraction, respectively) and possible orbit/eyeball asymmetry. See an oculoplastic specialist for evaluation. Treatment is available. See following video.

Eyelid asymmetry is commonly caused by eyelid ptosis, a condition on with one of the upper eyelids is lower than the other one, In some cases, the eyelid asymmetry is not caused by ptosis by exophthalmos, a condition on which one eye is more anteriorly protruded that the other one.Either condition could most of the time be fixed with plastic surgery.Patients interested in determining the cause of eyelid asymmetry  should make a consultation with a Board Certified Plastic Surgeon specialized in plastic surgery procedures of the face

Your problem is actually complex given that you have relatively large eyes.  Surgery on the eyelids can result in better symmetry but leave you with an unnatural appearance.  Carefully consider your options.