I wouldn't give it either. If you're covered by standing orders or something, that's different. But just to give it without an order is practicing medicine w/out a license. Believe it or not, I have seen people be allergic to Benadryl (geez, guess you're out of luck if you react to something else....). So you'd really be hung out to dry if that pt were one of the rare few c a Benadryl allergy. Then what do you tell the doc?
In any case, I think you're right. Good luck.