Can I turn my downturn eyes to upturn eyes? (Photo)

Repairing requires a careful consultation to determine what your best options.  Less more.  You need to find a fellowship trained oculoplastic surgeon.  Direct experience with double fold surgery is essential.  Your consultation should include careful measurements and a neosynephrine test.  If measurements are not performed, you are in the wrong office.

The inner corner (medial canthus) cannot be moved down but the other corner (lateral canthus) can be moved up, although I am not sure if it is really necessary in your case. You do have slight lower eyelid retraction with scleral show, which is probably what is bothering you.  It is best to see an oculoplastic surgeon for in person consultation to go over your concerns and possible solutions.

The internal muscle that opens your eyes are somewhat weak, a very common condition in many Asian eyelids. Your left eye looks slightly more affected than the right. This muscle is routinely corrected at the time of any eyelid crease operation in order to maximize the chances for a nice result. This is somewhat of a medium complexity case.