You tell them to treat you like you have addison's disease because you suffer from adrenal insufficiency, some ER doctors understand what adrenal insufficiency is.
I would steer away from the use of the term Adrenal fatigue. This is why it's always a good idea to have some hydrocortisone cream handy to put on the wrists in case your throwing up too much. i forget how to dose this, i'd have to ask this other group i use to be in about that, but in the ER they may pump u with Solu-medrol and also give you electrolytes via I.V.