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.

The position of the eyelid margin of the left upper lid is lower as compared to the right upper lid. This is termed ptosis (or blepharoptosis). There are different varieties of ptosis with different causes. Luckily, these are often corrected with the appropriate procedure.
With a history of ptosis on the other lid, you should see an oculofacial plastic surgeon who can evaluate your ptosis, rule out rare and serious causes of ptosis, and help you to find a solution.

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. 

If one has eyelid ptosis, one has drooping of eyelids below the limbus of the eyelid normally within 2mm. If you have true eyelid ptosis which droops down to your upper or middle then you should have both of them corrected simultaneously for an optimal result. These are completely different operative procedures.

 I agree, your left eye does appear to be ptotic.  It is best to see an occuloplastic surgeon to have this evaluated and treated. Ptosis surgery can be tricky so make sure your surgeon does this operation frequently. 

The higher position of your left upper eyelid crease is very suggestive of ptosis. One of the most common findings in ptosis is elevation of the lid crease. In many cases, ptosis is bilateral. If the left eye alone is corrected, there is potential for the ptosis in the right eye to be unmasked. I would recommend an ASOPRS trained occuloplastic surgeon.

Orbital asymmetry is a very common underlying issue in young people concerned about droopy eyelids. Consult an eyelid or orbital specialist to rule out any pathology around the eyes and then you can consider cosmetic bone or eyelid surgery if you want to change the appearance. Best of luck!

From looking at your picture, it seems to me that you may have asymmetry of your upper eyelids due to unilateral ptosis of the right eyebrow.  I do see drooping of the right upper eyelid compared to the left.  However, if you should lift the right eyebrow, and look again, both upper eyelids may look more symmetrical.  That is something that you should ask your doctor.

You have a very slight assymetry between the eyes. Asymmetry is the rule rather than the exception in most cases: Your right brow is silghtly lower, the left lid is borderline ptotic, ie it covers just a hair more of the upper part if the iris than the right lid and has a higher crease.  It is up to you  and the surgeon to decide to what degree you would like these corrected.