If we treat my child's blood in eyeball will it be gone, or do i need to keep worrying?

Bloody eye: Most blood on the surface of the eye, known as subconj heme, will resolve in 2-4 weeks on its own. Blood inside the eye, such as traumatic hyphema, requires professional follow-up with your local ophthalmologist, since other eye problems may arise.

Probably not: A red blood spot on the white of the eye may look scary but is usually not serious and will most of the time absorb by itself within a week or so. As long as vision in that eye remains good and unchanged and there is no pain it is fine to just leave it alone. If it is the result of an injury then it should be checked by an ophthalmologist if there's pain, reduced vision and/or sensitivity to light.