Is the asymmetry of my eyes fixable? (Photo)

Be careful trying to achieve symmetry that exists secondary to a congenital anomaly. If one looks at your photos, he/she should note that your entire bony orbit is lower on the left than on the right. Not only does it involve both your left upper and lower eyelids and your left brow, but the actual position/level of your left EYE is also lower. This is a bony anomaly that is congenital and after you spend lots of $, you will eventually learn that is will never be symmetrical without major bony reconstruction.   Fillers will augment  the cheekbone, raising the midface but you don't really have midface descent yet. Fat grafts can help smooth out the lower eyelid and add midface fullness, but they will not/cannot raise the bony orbit which is the culprit of your congenital asymmetry. Mild asymmetry is the norm rather than the exception and what you demonstrate is an example of being human. You don't look "old". Instead you represent an example of human norms. 

You have a difference in the anatomy of the bones here.  The whole left orbit is lower so that the eye is sitting at a lower level.  To fix this would entail orbital surgery to actually elevate the eye and entails enough risks that it wouldn't be worth it.  Adding volume to the cheeks will help the flatter cheek, but will not change the appearance of the eye.  

Most people are asymmetric if you look closely.  Based on your picture, you appear to have less volume of your left cheek and bony orbit.  Volume augmentation with filler or your own fat can improve asymmetries.  As long as you don't expect perfect symmetry, just improvement, you may find this beneficial."This answer has been solicited without seeing this patient and cannot be held as true medical advice, but only opinion. Seek in-person treatment with a trained medical professional for appropriate care."