One eye is sunken while the other is bigger and more alerted? What can be done? (Photo)

Eye asymmetry has many causes. See following video. It is hard to appreciate significant asymmetry based on your photos. Best to see an oculoplastic specialist for evaluation.

I do see the difference between the eyes. The difference is small and subtle, I'm not sure you'd gain much from any intervention. You can see a surgeon in person if you feel the photos don't do it justice. Best wishes. 

It all depends on why things are the way they are.  If you'd had facial trauma where the bones around your eye were broken, this could potentially be fixed with surgery.  If it is a congenital facial skeleton issue (meaning you were born with it)  then it's going to be really difficult and definitely not worth the correction you're trying to achieve.  Unfortunately either way you're talking about surgery but if you came to me I'd start with a facial CT scan to look at your bones.