Eyelid Ptosis or Extra Skin?

Often, asymmetry of the eyes is not due to ptosis, but due to orbital dystopia. That is a different "set" of the eyeball within the bone. One eyeball is literally deeper in the bone than the other.
In your case, it appears that the right eye "bulges" more. This causes a chain reaction. Often lower eyelid fat is more visible, there is more white showing below the pigmented portion of the eye, and the eye appears "bigger". The lid creases also appear different, since there is a different shaped eyeball pushing on them from behind.
This circumstance cannot, under most circumstances be corrected. It can only be camouflaged, or be made to appear less prominent.
I personally do not believe you have ptosis alone, but definitely appear to have one eye that is deeper set than the other.
There are many methods for camouflaging eye asymmetry, from asymmetric eyelid lifts to ptosis repairs to asymmetric browlifts to an asymmetrically performed superficial cheeklift, minimal incision (USIC).
A patient must first understand that these are all not curative procedures, but designed to camouflage the orbital dystopia.
The attached paper shows three patients who had deliberate alteration of eye shape to reduce (camouflage) the appearance of a prominent globe.

From your photograph it appears that you have ptosis (drooping) of the left upper eyelid. An oculoplastic surgeon could perform a relatively fast procedure to elevate the lid to match your other eye. Healing time is a couple of weeks and most patients do not bruise significantly. 

Your pictures suggest that your primary problem is related
to asymmetry of your underlying facial bones. In your case, you’re right
superior orbital rim sets at a lower level than the opposite side. This is
commonly referred to as “orbital dystopia”. When this occurs, the eyelid soft
tissue is secondarily effected with resultant eyelid asymmetry.

                  I
would not recommend treatment for this type of mild deformity because of the
risk benefit ratio. When the potential for improvement relative to the
complication rate is minimal this is not a risk worth taking.

                  There
are a variety of causes of orbital asymmetry. It may be related to the boney
orbit, the eyelid or the eyebrow. In most cases of mild asymmetry there’s some
asymmetry of the bones surrounding the eye. This cannot be treated without
major surgery. If you continue to have concerns about your asymmetry it’s appropriate to consult a board certified plastic surgeon.