Could a mild case of anaphylaxis go away on its own with no medical intervention?

Yes: When a person is experiencing early anaphylaxis symptoms, the body's response is fight/flight which releases adrenaline. The treatment for anaphylaxis is Epinephrine which is adrenalin. Frequently patients report it was the Benadryl (diphenhydramine) that made the anaphylaxis better, not realizing it takes over an hour for Benadryl (diphenhydramine) to reach a serum level that will block histamine.