Bleeding on white part of eye what should i do ?

See below: You may have a subconjunctival hemorrhage, which could be secondary to rubbing your eye. Although looks ferocious, these are self-limited, non-progressive and reverse over a few days. You neglect to mention if you are taking medication even aspirin, as these could play a role. See an eye doctor if this is causing loss of vision, double vision, or excessive worry.

Subconj hemorrhage : Usually this is a “subconjunctival hemorrhage”- painless bleeding under the top layer of the eye: most often from internal pressure like nose blowing or straining with bowel movement. If not affecting vision (usual it does not), not painful, & not enlarging, no need to do anything but wait till blood cells dissolve. If a recurrent issue for no obvious reason, see Dr for possible underlying cause