Should the allergist have given me an Epipen (epinephrine) for my new basil allergy? Also, my symptoms came back 3 days after I ate basil. Should I be worried?

Likely unrelated. First basil allergy is likely extremely rare. 2nd allergy to food usually occurs within 2 hrs (up to 10 hrs with red meat) and your reaction after 72 hrs is not from basil . Thus I would look for another culprit. EpiPen (epinephrine) should be available if you have had an anaphylactic reaction regardless of what might have caused it. If you did not have one, then EpiPen (epinephrine) is not needed .