Facial asymmetry - Eye is significantly droopy and right side of my face pulls to the side. What's causing it? (photo)

There is no substitute for a detailed in person examination. You have a high upper eyelid sulcus and a compensatory eyebrow elevation. It is likely that when your eyebrows are relaxed the upper eyelid are heavy. Surgery to correct the upper eyelid ptosis can address this provided you get the correct upper eyelid ptosis surgery. If you are using prostaglandin contain eyelash growth products, these are harmful to the eyelid. They cause damage to the fat in the upper eyelid and a type of scaring in the eyelid tissue. Latisse is perhaps the best known of these products. However, there are many over the counter eyelash growth products that contain isopropyl cloprostenate. Don't use them.

I believe that a lot of options are available to you, such as Threading or Radiofrequency on that side of your face, however, I would need a face to face consultation and proper examination before giving my final opinion, because in certain cases the only real remedy can be a Facelift.

If for no other reason, that would put your mind at ease, you might consider having a neurologic evaluation. Assuming that it is normal, you might conquer with an expert facial plastic surgeon to consider your options. Minor asymmetries are completely normal, but you should explore your options which could be as simple as injectable fillers.