I've received small red dots. underneath my eye. what are they? or how can i prevent them?

Red dots: The red dots could be many different lesions. You should see an eye doctor for further evaluation. Red dots on the skin are most commonly hemangiomas which can be lasered away.

Red dots: I think you are saying the red dots are under the eye and on the eyelid. If new, they could be inflammatory (dermatitis), allergic, or a localized infected or blocked gland. If the red spots are on the eye itself, they are probably just from a small broken vessel on the conjunctiva which will clear spontaneously. In either case, see an eye doctor to make a diagnosis and suggest treatment.