The membrane over my eyeball has started sliding around and has caused a wrinkle on my eyeball. What could this be?

This is challenging to answer since it depends on what part of the eye you're talking about. There are a number of layers to the eye, none of which can actually slide around, but some layers can change shape or move/shift. The conjunctiva is the outer lining of the eye and it can swell over time causing a condition known as conjunctivochalasis. If this has caused symptoms of tearing or discomfort, the lining can be tightened to relieve the swelling with a procedure known as a conjuctivoplasty. Epithelial basement membrane corneal dystrophy can cause corneal erosions (when the outermost layer of the eye does not stay attached to the tissue beneath it) which may give the feeling of sliding. The outer corneal cells are loose and can change the vision or create a wrinkle in the outer cornea. A lens implant placed after cataract surgery can also develop a wrinkle in the posterior capsule, also called a "secondary cataract." This is common and easily treated with an office procedure known as a YAG capsulotomy. All these conditions have a great prognosis but you may want to call your eye doctor and move up the appointment if your vision is worsening so they can treat you now.