Broken Blood Vessels in your eye can be caused by a number of things that cause your blood pressure to rise which then results in the ruptured blood vessel in the eye.
Some common things that cause your blood vessel in your eye to break and burst are constipation, straining when trying to poop, laughing, stress, sneezing, coughing or anything else that could cause even a temporary rise in blood pressure.
Also if your blood pressure is constantly high then it can lead to a broken blood vessel in your eye.
If the broken blood vessel in the eye is not too serious then it will usually heal on it's own within a week and if not you should see an eye doctor about it or go to the emergency room.
Usually though the broken blood vessels in your eye will heal on their own naturally.