A broken blood vessel in the eye, known medically as a subconjunctival hemorrhage, is a very common and almost always a benign medical problem. However, it is important to get a general check up from a primary care doctor
to make sure it's not something serious. The small blood vessels that run below the conjunctiva (the membranous covering of the eye and eyelid) are very fragile. They can be ruptured for many reasons. Obviously direct trauma to the eye can cause the blood vessels to rupture, even extremely minor trauma like rubbing an eye too hard. Many things that cause these delicate blood vessels to rupture involve straining, which temporarily increases blood pressure in veins. And because of this, subconjunctival hemorrhages tend to be a side effect of other problems. Subconjunctival hemorrhages can come along with a cold (which causes a lot of coughing and sneezing), constipation (which causes a lot of straining), childbirth (again, straining), falling or otherwise injuring yourself (people tend to strain very hard as they get injured), GI illness (straining due to vomiting
and bowel movements). Other less common causes of subconjunctival hemorrhage are very high blood pressure
and problems with blood clotting or increased levels of anticoagulant medication. In your case, a subconjunctival hemorrhage could suddenly appear overnight for these reasons: you rubbed your eye violently in your sleep, you sneezed or coughed hard in your sleep, something happened at the end of the day that caused it and you did not notice it till morning, or (less likely) you have a medical condition like high blood pressure or a blood clotting problem that caused it to occur spontaneously. The hemorrhage itself is harmless and will resolve on its own over a few weeks. Again you should get a general check up from a primary care doctor to make sure you are not developing a problem with high blood pressure or, rarely, blood clotting.