I would recommend that you have this checked out by your pediatrician
as soon as you can.
The most common cause of blood in the white part of the eye is a subconjunctival hemorrhage. Most of the time, these are caused by crying or other straining which bursts one of the small fragile blood vessels in the white part of the eye. When this happens, some blood leaks out and you get the bright red appearance in a patch. Most subconjunctival hemorrhages are benign and don't need any particular treatment.
However, before saying this, it is important to examine the eye closely to make sure that there is not a more serious form of eye trauma or other cause of this bleeding
. Your pediatrician can examine your child closely to make sure the eye is ok. They can also make sure there are not any other signs of easing bruising or bleeding elsewhere on your child's body.
If this is just an isolated subconjunctival hemorrhage, they will probably just recommend close observation. However, if there are any other concerning signs, they may want to perform additional testing.
Contact your pediatrician's office and make an appointment as soon as you can.