Hello Adam,   The classical diagnosis for the symptoms you describe (chest pain, shortness of breath, and different blood pressure in each arm), is that of an aortic dissection.   The aorta (and other arteries) are made of several layers of different types of cells.  The inner-most layer, called the tunica intima (the one that comes in contact with blood) is relatively thin.  With chronic high blood pressure, a small defect in the intima can propagate into a large tear between the this layer and the next, called the tunica media.  Because the blood is forced between the two layers and separates them, this is called a dissection.   Depending on the location and extent of dissection, treatment can range from medication to treat high blood pressure to surgery to repair the damaged artery.   To your health, Neil MD