Can a person be allergic to epinephrine?

No, but sensitive: Epinephrine, or adrenalin, is a normal stress hormone in your body so you cannot be, strictly defined, allergic. But you certainly can be sensitive to the normal physiologic responses to epinephrine, especially in higher doses. So one may experience fast heart rate, anxiety, sweats, high blood pressure, irregular heart beats, which may be perceived as "allergic" reactions, but actually are not.

Unusual: But can rarely occur. Usually the allergy is to a compound in the medication.