After an hour of research:
It seems like the base rate of anaphylaxis from bee stings is about 3%. Anaphylaxis, if it occurs, usually starts within minutes of the exposure to the allergen. (It can occur as much as 24 hours later, but this is "rare". I don't know how rare, quantitatively.)
Anaphylaxis is the result of a "global" or "systematic" reaction, as opposed to a "local" reaction, namely swelling around the area stung.
There is some risk that a local reaction can cause swelling of the throat blocking the airways, but since 43% of bee stings are on the face and neck, and severe respiratory distress is rare, this is is very uncommon. It seems like this is only a concern when the person is stung inside the mouth or throat.
The simple answer is observation.
As long as there's no difficulty swallowing or breathing then the reaction is local only. People with true anaphylaxis experience facial/tongue/mouth swelling and respiratory symptoms regardless of where the sting is.
Any respiratory or oral symptoms should prompt an immediate trip to the hospital.
In such a case, you might get many of the benefits without the covid risks from driving to very close to the ER, then hanging out there and not going in and risking infection unless worse symptoms develop, but being able to act very fast if they do.
From medline plus:
Most severe allergic reactions occur within seconds or minutes after exposure to the allergen. Some reactions can occur after several hours, particularly if the allergen causes a reaction after it has been eaten. In very rare cases, reactions develop after 24 hours.
Anaphylaxis is a sudden and severe allergic reaction that occurs within minutes of exposure. Immediate medical attention is needed for this condition. Without treatment, anaphylaxis can get worse very quickly and lead to death within 15 minutes.
It seems like if you don't have a severe reaction, shortly after the sting, anaphylaxis is pretty unlikely?
But I think that this is with allergens in general, and according to medical news today, swelling from bee stings can occur gradually over the course of 24 or 48 hours.
I'm glad you could already find the answer for it, and I hope your dad gets better.
I'm writing just to say something that has worked for me (I'm also allergic). When I was stung by a wasp, I found that applying a cold compress reduced the swelling considerably, and I recovered in a matter of hours. When it happened before and I didn't use the cold compress, I remember it taking days to recover, and I could not walk properly while it was swelled. Both times I was stung on my ankle.
This paper seems to be exactly what I'm looking for. It deals specifically with airway obstruction as a result of local swelling.
Approximately 43% of Hymenoptera stings occur in the head and neck region, but only nine cases of Hymenoptera stings in the oropharyngeal region have been described. None of these victims experienced systemic symptoms, but all of them developed some degree of localized swelling. The majority had uneventful recoveries after treatment with a combination of anti-histamines, corticosteroids, and epinephrine. One patient required nasotrachealintubation because of theseverity of his airway swelling. None of the stings resulted in death.
Facts:
Questions:
[Update: it seems like the base-rate of anaphylaxis from bee stings is 3%, when anaphylaxis occurs, it usually starts within within a few minutes.
The key question I have left is if "large local swelling", can block the air ways when it the swelling is on the head or face.]
Thank you!
Eli