Of course the heart is effected, it increases. However s does the heart rate increase when you run on the treadmill.
The primary concern of a child having a severe allergic reaction is not the heart rate. Rather a clear airway and normal blood pressure.
Heart rate does get effected, but in a normal healthy person that’s not a big concern. The major concern is once the Epi wears off and the symptoms come back.
Of course the ER will do cardiac monitoring, usually for around 4-6 hours but that’s not the real concern.