Weak veins. Subconjunctival hemorrhage is due to leakage from fragile veins in the conjunctiva. This can be caused by rubbing the eye, sneezing, straining and light trauma. Frequently no cause is identified. Almost always it is benign and will absorb with no consequences. See your ophthalmologist if it is recurrent.
Usually benign. Broken blood vessels on the surface of the eye (subconjunctival hemorrhages) are very common. They are more common in individuals treated for high blood pressure, or those patients using blood thinning medications called anticoagulants. They can be caused by a simple sneeze or cough, or rubbing the eye inadvertantly while sleeping. If recurrent, have BP checked and blood clotting tests done.
Bleed. This is a sub-conjunctival hemorrhage. As long as the vision is unchanged and there is no pain, everything should be fine. If it is a little irritated, then you can use an artificial tear up to 4 times a day to lubricate. This is due to a blood vessel leaking blood and is usually without cause. Sometimes straining or blood thinner can cause this. If it continues to happen, follow up with eye md.