Duanes Syndrome with a Droopy Eyelid? (photo)

You appear to have droopy eyebrow more than droopy eyelid, although it is difficult to assess fully from a photo, so see an oculoplastic surgeon.

My oldest son has Duane's syndrome and there is no relationship with brow and upper eyelid ptosis. Best to seek IN PERSON examination by an oculo plastic surgeon in your area. There are surgical options to aid the improvement in upper lid and brow appearance. 

While Duane's syndrome is an eye muscle disorder, you do have a lower brow, upper eyelid hooding and apparent eyelid ptosis of the affected side. You would benefit by a transpalpebral browlift (given you are a male and your lack of a frontal hairline) and eyelid lift surgery to remove the hooding of your right eye. That eye may also need a ptosis repair although this one picture alone is not adequate to fully answer that question.