Red, veiny eyes?

[Exhausted777]

What does it mean when my eyes are ALWAYS red & veiny?  My right eye is particularly bad, with permanent veins going from the inner cornea to the green part.  Not a burst blood vessel or a red starburst, but one prominent vein right through the middle.  I had lasik eye surgery 4 yrs ago & asked the eye doctor.  He dismissed it as nothing of concern.  Lately I've noticed my eyes having more of these pronounced red veins.  Is this something that should be of concern, or do some people have "veiny" eyes, moreso than others?  I've noticed my older daughter has a lot of prominent veins in her eyes as well.  Trying not to freak out, and trying hard not to google!