My dog won't eat and her tongue is hanging out. Is it an emergency?

These symptoms indicate that your dog is very ill. She really should be seen by a vet asap for a full examination and potential bloodwork to find out the underlying cause of her symptoms. Especially since she won't take anything by mouth. Try offering her small amount of Pedialyte and Ensure using a small turkey baster or syringe for now, until you can get her in to the vet. If your dog isn't spayed, there's particular cause for concern. Shortly after un-spayed females have their menstrual cycle they are at high risk of developing an infected uterus causing a condition called pyometra, which can be life threatening if not treated. So it really is best for your pet's health to get a diagnosis quickly and treated by your vet.