Benadryl is a standard operating procedure medication they give you when you get a venomous snake bite. It's administered sometimes prophylactically for a potential allergic reaction.
But not from the bite.
Example - in the case of rattlesnake, copperhead, and cottonmouth envenomations, Antivenin (Crotalidae) Polyvalent has long been the standard treatment. However, ACP is known to be highly allergenic because of its equine basis and often poses a greater risk to the patient than the snakebite itself. In a study, anywhere from a quarter to a little more than half of patients who received ACP had allergic reactions including anaphylaxis.
The sheep bases antivenin CroFab has a better track record as compared to ACP.
When I got bit by one of my heloderma, the doctor put me on Benadryl - didn't do a thing. It was administered via IV. At the time I asked the administering doctor why I was getting Benadryl and was told it was SOP. The damn drug made me really edgy and nauseous. I asked a second doctor why and he told me that the admitting doctor made a mistake - and confirmed that antihistamines were administered in conjunction with the antivenin for snake bites.
Bottom line is this: allergies to opistoglyphous snake venom are almost unheard of. Allergies to front fanged snakes are slightly more common because the residue that is sometime dribbled or leaked during a prey strike can dry and then be inhaled over several years time - leading to an allergy. If you have a real allergy to snake venom, the best course of action is to have an epipen on hand.