After serious vomiting, drinking or coughing may cause the broken blood vessel in eyes which is also called subconjunctival hemorrhages. If it is not that serious, it may recover about a week. During this time, you should use the towel with cold water to cover on your eyes at the first several days and then change the towel with water of mild temperature to cover. That can be cured. If this symptom is serious, you'd better go to see the doctor and have a check.
The broken blood vessel in eyes is also called subconjunctival hemorrhages. And the broken blood vessels acts like any bruise on the skin and often take around a week or so to clear. Sometimes, it even causes significant pain or changes in vision. If so, you'd better get your eyes treated by an eye doctor immediately for the sake of your eye health.
Long time using of the eye will lead to eyes fatigue and blurred vision. Please pay attention to relaxation and have a good rest. Eye drops of artificial tears will help you a lot in a short time. Doing massage by yourself every after two hours' eye use and watching far distance view from the windows. Vitamin B2, vitamin A and C will also help in a food way.