What are some causes for red spots on my eyelids and under my eye?

Rash?: Some skin rash secondary to make up use, eczema, dermatitis etc....You should provide more specific info...Such as how long you have had this, what makes it worse or better, any new skincare/make up product?

Airborne: Rashes immediately around the eyes, in my experience, are nearly always caused by dust, pollen, and other airborne allergens and irritants. Your eye sockets are natural "cups" that trap airborne particles, and the skin in those areas is thin and sensitive. Makeup used to be a common cause of such rashes but not any more; the cosmetic companies have largely eliminated allergens from eye makeup.