A broken blood vessel in the eye, otherwise known as subconjunctival hemorrhage, is caused by a rupture of the conjunctiva vessels at the surface of the eye.
It can be caused by trauma or can occur spontaneously. Although it looks alarming, it almost always benign and the blood will absorb spontaneously within two weeks. More often than not, it comes without any symptoms.
However, if you find that this condition often recurs or does not go away after some time, it will be best to seek an eye doctor's opinion who may look into your drug medicine history or conduct a blood test to investigate the problem further.