No problems, ever with Epi-pens
and I've traveled a great deal.
As I live in a place that is very hot in the summer, I take precautions with mine and carry them in a special pack made for diabetic medicines called a Frio pack. It doesn't use ice (which is a bother when traveling). You soak the inner lining in water and the evaporation of that water keeps your items from getting too hot.
I think the TSA folks have seen a jillion Epi-pens.
I do carry along the original packaging.