Yes, it is possible for to get the broken blood vessels in the eyes because of the high blood pressure. The high blood pressure is to point to artery systolic blood pressure and or diastolic high pressure in the resting state. The high blood pressure is a kind of to arterial pressure rise for characteristic which may be accompanied by cardiovascular brain and kidney organ such as functional or organic change of systemic disease. And in the high blood pressure, the blood vessel in the eyes may be broken. The subconjunctival hemorrhage is subconjunctival vascular rupture or vascular permeability of the increased bleeding. The bleeding reason can include trauma, head, neck extrusion, severe cough, conjunctival inflammation and hypertension, arteriosclerosis, nephritis, diabetes, haemophilia, sepsis, malaria, typhoid fever, cholera and other systemic disease. However, after the blood vessels broke under the high blood pressure, you'd better go to see the doctor and accept the treatment.