Broken blood vessels in the eyes, causing red spots to appear on the eyeball, can occur for a variety of reasons. Unless blood finds its way into the pupil or iris, there is generally no danger.
The small blood vessels under the membrane that covers the eyeball, called the conjunctiva, can rupture due to any number of daily occurrences, such as sneezing or coughing. The condition is harmless and symptoms usually subside within a few days without treatment. Taking a daily dose of 200mg of vitamin C can help strengthen the vessels and prevent recurrence.
Blood vessels between the pupil and iris can break from trauma to the eye. Called hyphema, this is a serious condition, which can result in glaucoma and permanent loss of vision. It requires immediate medical treatment.
Diabetics are at risk for diabetic retinopathy, the breaking of the blood vessels of the retina. Symptoms include seeing spots and having blurry or hazy vision. Diabetics should seek immediate medical attention should these symptoms occur.