This is the second time a vein in my mom's eye that pops, should she go to the dr to get checked and why does it keep happening?

Eye hemorrhage. There could be several reasons she could get a broken blood vessel in the white part of the eye. She should get checked for high blood pressure or a bleeding problem. Most reasons are not serious. The bleeding may come from rubbing eyes too hard, coughing or sneezing, straining from heavy lifting and vomiting. Sometimes, no reason is found. It usually clears up in time.