This condition is termed as Subconjunctival hemorrhage. Well, the exact cause is unknown, but due to sneezing, lifting, vomiting , blood vessel can get rupture.
The blood in the eye, will get absorbed in 1-2 weeks. N
o medication is required to do so. But my opinion is that you should be examined by doctor, to rule out any serious bleeding disorder. So please get checked from doctor.
Well, in case a person is taking blood thinners, Severe thoracic trauma, severe hypertension , to name a few. also usually such incidents are not so common. In your case, most likely you are safe.
Take care. and Happy Holidays.