Auto-injectors are a device to administer an injectable preparation into the skin without the skills that a professional such as a doctor or nurse would have. They are designed for yourself and myself, as members of the public, to use. And the auto-injector as a pen has the dosage, a unit dose of medication that is required.
The storage requirements are that they remain within the packaging that they come. That they are safety, that they function correctly when you pull them out of there. Do not open them and store them outside of the container that they come in. Do read the instructions carefully as to how they should be stored in the temperatures.
In general, they can be carried everywhere, but do not leave them on the windscreen of your car, do not leave them in the refrigerator with your sandwiches. Do make sure that you read that and follow the instructions on there. Always carry them in the original container that they have been supplied in.