No insurance. Student debt. Lousy pay. Long hours. How can I take care of my chest trauma?

Rest, ice and.. ...Pain relievers (tylenol (acetaminophen) or Ibuprofen for example). Wait...This all assumes you are not seriously injured. By chest trauma are you referring to sore ribs from wrestling your friend, or major blunt chest injury with lung contusion, bleeding etc., if its more the latter, get to the hospital, insurance or not.
ER or urgent care. Depends on the type and severity of the chest trauma. If less severe, then an urgent care clinic at a general (or county) hospital may be enough. If more severe, then an emergency room at a general (or county) hospital.