First, there are large number of disparate issues that need to be addressed with your concerns.
Yes, there is something going on between the two eyelids. You are showing more left upper eyelid platform on the left side and there is a flare to the left eyebrow. This suggests that there is ptosis of the left upper eyelid. This ptosis is not well demonstrate in the photos but on examination it is often possible to assess and measure the basis for the asymmetry in the two side. A careful and detailed examination by a fellowship trained oculoplastic surgeon should establish why the two sides are asymmetric. The examination should also establish the best approach for dealing with the asymmetry.
Now, the other issue is assuming that the asymmetry was corrected, will it satisfy what you are looking for? I am not sure the two things are the same. If eyelid surgery to make the two eyes more symmetric will make you happy, then surgery will likely be the right choice for you. If you expect the surgery to make you look like the photoshopped models, I don't think that can be promised.
Correction of small eyes
When you consider plastic surgery it is important to consider not only the upside, but the downside of a procedure. Although you eyes appear to be a little shorter than some of the pictures of the models you selected, they certainly appear attractive and probably make visual sense when we look at your entire facial structure. Although there are many procedures described to change the tilt of eyelids and potentially lengthen them, there is a wide variation in the actual results, so that surgery might leave you with more asymmetry than you started with ( which is quite minimal). Rather than surgery, consider a consultation with a skilled make-up artist, who will help you achieve the effect you are looking for without the downside of surgery.