Looking for a job that consist of going all over the country to help people after natural disasters?

Your intention is noble. Unfortunately, I don't think the Red Cross or other disaster relief agencies employ medical technologists much. If I'm not mistaken, medical technologists spend most of their time in the lab.
A medic or a corpsman does this type of thing, which can include working in a field operating room and stitching some wounds. In MHO the military offers a great way to do this. Outside the military you must pay for schooling. In the military you get free room and board and pay to become a medic.