Thrombolysis is when a vein becomes inflamed. This can make the vein hurt and often appears int he leg or arm. If the pain does not subside, it should be looked at by a doctor. varicose veins can also be the cause of painful veins in the arm. This can be taken care of by a doctor. Even if the pain does subside, one should consult their doctor to find out the cause of the pain as there may be something more severe going on.