Before we answer that question, let's ask why we given it in the upper arm in the first place!
1) Easy to access
2) Easy to monitor for any adverse reaction
3) All the good studies done are based on injections administered to the upper arm
4) No good studies performed determining whether injections done at other body sites has equal efficacy to the arm.
5) If anaphylaxis occurs, a tourniquet can be easily applied to the arm proximal to the injection site which theoretically would decrease allergen traveling systemically