Do I have extra skin above one eye?

Your right upper eyelid/brow area is more hollow that the left side. The skin "collapses" on the more hollow side, similar to deflating a balloon. See an oculoplastic surgeon for evaluation. If simply due to fat loss, fat or filler injection to the right side can help greatly.

I do not think that you have a ptosis here, as the lid seems to be at the same height above the pupil on both sides.  You may have a slightly higher brow on the right.  You do have a difference in the crease.  You have more fat on the left behind the skin, so there is just the one crease.  On the right, you have less fat, and therefore a double crease  and a deeper appearance to the upper lid.  You should have an evaluation with an oculoplastic surgeon who can help you decide how best to improve the symmetry.

Based on your pictures, the eyes appear to have the same size, but the upper eyelid skin looks different. An in-person evaluation by a Board certified plastic surgeon, facial plastic surgeon or occuloplastic surgeon may be the best way to evaluate this.