If you were placed on warfarin (Coumadin), you need to get your blood checked once a month. This medication has a narrow safety margin. If your blood is too thin, you could have serious internal bleeding. If your blood is not thin enough, the drug will not work well and your DVT could get worse, or you could develop a more serious condition called pulmonary embolus. The FDA recently approved a new drug for the treatment of DVT called Xarelto. This medication does not require blood tests.