The burst blood vessels you're describing are called "subconjunctival hemorrhages." They occur among the many small and fragile blood vessels in the eye's conjunctiva, the clear membrane that covers the whites of the eyes and lubricates and protects the eyeball.
When one of these tiny blood vessels bursts, you will notice a bright red or dark patch on the whites of your eyes. A blood vessel can burst as a result of any number of normal, trivial occurrences - sneezing, coughing, straining, crying, vomiting, rubbing your eyes, but most of the time, no obvious cause can be identified. There are rarely any other symptoms, although sometimes you may feel some pain or mild irritation.
You may be at greater than normal risk of these little hemorrhages if you're taking medications or supplements that thin the blood, including warfarin (Coumadin), aspirin, Plavix or high doses of vitamin E or fish oil, or botanicals such as garlic. High doses of ginger, St. John's wort, ginkgo biloba, or cayenne may also increase your risk, although these are rare occurrences and do not typically occur with the standard dose for dietary supplements or the amounts usually used in foods. Sometimes, the burst blood vessels are associated with high blood pressure or with conjunctivitis (an eye infection).
Most of the time, the signs of the hemorrhages clear up without treatment, usually within 10 days. You may be able to prevent recurrences by taking vitamin C, 200 mg a day, which helps strengthen the walls of little blood vessels, and by taking grape seed extract or pycnogenol, which contain antioxidant pigments that do the same. Consult your doctor if you experience pain in connection with a subconjunctival hemorrhage, if you notice any changes in vision, have a history of a bleeding disorder or high blood pressure, or have injured your eye.
Andrew Weil, M.D.