My eyes are too high up on my face. Is there a procedure that can make them lower?

Thank you for your question, although it is a bit unusual.  Please submit a photograph of your entire face so that we can evaluate your facial proportions.  There are certainly options available to improve the shape of your eyelids and remove excess skin and fat.  Please see a board certified plastic surgeon to have your questions answered.  

You should know that yours is an unusual concern.It may be that you have a true issue that can be addressed with standard eyelid surgery.  However without a photograph, it is impossible to answer your question.Before you rush off to the cosmetic surgeon, ask yourself how many hours a day you spend thinking about this issue, if you avoid social situations due to this concern, or suspect that others are talking or making fun of your appearance.  These are often indicators of a body preoccupation that can be consistent with body dysmorphic disorder.

You are asking us to make comments and offer suggestions regarding your facial proportions without any idea of what you look like. That would be completely impossible. It would take full face photos front and side at a minimum.