I have been getting tiny purple veins below my eye and also on the other eye around it i have a big green one. how do you get it to go away?

Blood vessels: Thin skin under the eye can allow superficial blood vessels to become visible. This is anatomic -- just part of the way your body is made.

Periorbital eye vein: Veins around the eyes (periorbital veins) are common and can be treated by sclerotherapy if large and microneedle RF or Laser if small. Sometimes I use a combination of both treatments.