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Is it on the white of the eye?
It is called a subconjunctival hemorrhage (as you said, a busted blood vessel). This is harmless to your eye and vision. It is caused by many things: trauma (in your sleep or rubbing), straining (coughing, constipation), high blood pressure. Rarely, it can be caused by clotting disorders. You do not need any treatment for it.
I hope this helps and thank you.