Some causes of broken blood vessels in the eyes are severe coughs, strong sneezes, vomiting, lifting heavy weights and straining according to the Mayo Clinic. In some cases, there is no cause for this problem. The rupture of a blood vessel in the eyes is called a subconjunctival hemorrhage.
A subconjunctival hemorrhage is a bright red spot that forms in the conjunctiva. The conjunctiva is the transparent layer that covers the white part of the eyes. Because a subconjunctival hemorrhage will resolve on its own, no treatment is necessary for it according to WebMD.
When blood accumulates in the anterior chamber (the space between the cornea and iris), it also can cause a red spot. However, this eye condition is called a hyphema and can be more serious. Often caused by a trauma to the eyes, a hyphema may require a visit to the ophthalmologist.
If you experience any eye problems, you should seek proper medical advice for your specific condition.