Maybe I worry too much, but I want to know how blood in eye will affect my child's overall health.?

Blood in the eye. Blood in the eye can mean several things. If the eye has recently suffered trauma, a hyphema may result-- this needs to be followed carefully for a week or more, since it may result in increased pressure in the eye or decreased vision. Blood on the surface of the eye is likely a subconj heme-- this will resolve in 2-4 weeks by itself. Blood in the retina needs follow-up locally.
Hyphema. Blood in the eye or hyphema, usually comes from trauma to the eye. If there is no ocular problem resulting, it should not cause any general health problems.
Blood in eye. You would have to be more specific about where the blood is located and how it got there. If it was through an injury the eye has to be examined carefully to see if there are internal injuries to the eye. But the term blood in the eye is too vague to give a good answer.