By "on the eye", I am assuming that it is on the conjunctiva
. It does seem to be a malformation of the conjunctival blood vessels, that may have occurred from before birth while the baby was developing inside her mother's womb. Which means that it is a sort of birth mark, but since you are certain it wasn't there until she was 18 months old, it could be something that developed in response to a mote of dust or something that went into her eye and sort of stuck there and caused an inflammation.
If, however, the red mark is outside the eye and on the skin, it is most likely a birth nevus
or a hemangioma: this would behave in the way you describe: it would enlarge in the first few years and start shrinking only after that. These types of marks are common, and as you rightly say, they shrink later on, but it isn't a right thing to think they increase in size around puberty
Perhaps you could send an image to me at my email id? email@example.com
Taher Kagalwala, Mumbai, India