I have burst blood vessels above my left eyeball?

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.

Subconjunctival heme: It is due to a small blood vessel outside the eye but under the lining of the eye (conjunctiva) busted. It is called subconjunctival hemorrhage and usually spontaneous (not related to any underlying diseases). It is usually self-limited and will resolve in a few days without treatment.