Epipens have the side effect of making the heart race, and they also give
you a sense of panic. After all, it is causing your body to release more
adrenaline, which is one of the cheif biochemical components of panic.
Without warning, it's normal to mistake that panicky feeling for real panic
and take it futher, hyperventilating, etc.

Your precautions with the antibiotic are justified. It would be even better
to have someone else administer the antibiotics.

Also, don't forget to have the child's lips and hands washed after taking
the antibiotic. It would be truly awful for him to give you a fatal kiss.

Twenty minutes is about right. I'd also ask for an antihistamine to take at
the same time - it might give you even more time.