You MUST have the solu-cortef.  If this endo won’t give you the prescription, find another one who will.  He is being irresponsible.  It won’t matter if your child is with you or not if you need the shot and don’t have it.  You may be near a hospital at home, but what if you are away from home?  Illness and accidents can happen anywhere and usually do.  My daughter got sick one night in a hotel room in Georgia on the way down to Florida.  I didn’t even know what city I was in much less where a hospital was.  To my way of thinking, this borders on malpractice.