I think I have a burst blood vessel in my eye, is there anything I can do to make it clear up faster? I have had this problem before, it is a red blotch in the corner of my eye. It is not painful but it looks awful. I think it happened when I coughed real

No. You can see an eye doctor for recommendations or see your family physician for treatment for cough to prevent more occurrences.
It . It is a benign condition that frequently occurs from any kind of strain, such as coughing, lifting anything heavy, sneezing, even rubbing the eye. People with high blood pressure as well as patients on blood thinners are at higher risk. There is nothing to do other than wait for the blood clot to dissolve on its own. However, if this recurs multiple times, you must be evaluated for clotting disorders. Hope this helps!