Answer: What a difficult case! This is definitely a case which nicely describes some of the grey areas in medicine!
The short answer would be that if you ask multiple physicians for direction on this, you would most likely get multiple answers. Judgment and experience here are the key.
You describe limited evidence of anaphylaxis apart from a history of same and a new possible exposure. The patient has no rash, no significant swelling, no wheezes, no vomiting or diarrhea. It is possible that the patient was having anaphylaxis and did require epinephrine however it is difficult to know.
Seizure would be an uncommon presentation for anaphylaxis unless the patient was profoundly hypotensive or hypoxic as to the underlying cause (which may have been the case here given the lack of a seizure history and the non-obtainable BP: so maybe it was anaphylaxis…or was that lack of an obtainable BP on the basis of agitation…).
The other consideration would be that perhaps the patient did not have anaphylaxis and was given epinephrine and then seized because of a hypertensive reaction and is now agitated and post-ictal.
Those would be our thoughts.
In terms of action, we probably are not going to be able to determine on scene the underlying pathophysiology, and the patient has no obtainable BP and needs transport.
Our direction would be to load and go, patch to BHP en-route for consideration of epinephrine and other interventions and therapies. Our bet is that different BHP would each suggest something slightly different: such is the essence of medicine.