Is there such thing as red eyeshadow?

Yes. Theatrical make-up such as MAC, MakeUpForever, etc. have red powders you can use as eyeshadow. The reason that you don't see it that often is MANY people are allergic to red pigment, especially around the eyes! Also, red around the eyes looks terrible- like you are sick or have been crying. But if that's the look you want- Go for it! Just remove if the color starts to irritate your eyes. Good Luck!