Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Riggs swallowed a bee stinger.
My hope is that the stinger makes its way down into his stomach where his stomach acid should dissolve the stinger and neutralize the venom. It may however get stung in his esophagus, and that could lead to painful swelling and difficulty swallowing.
Is his breathing rate and activity level normal?
Any vomiting or diarrhea?
Any difficulty breathing due to facial or neck swelling now?
I would not wait to see his reaction, I would pretreat him now as a precaution.
You can give him Benadryl (diphenhydramine only don't use the combination products with decongestants or acetaminophen as they can be toxic for dogs) at a dose of 1mg to 2mg per pound of body weight or one 25mg capsule per 15 to 25 pounds of body weight orally every 8 hours. You'll need to give it for at least 72 hours (3 days) to allow the allergen time to clear. If you stop too soon the reaction may recur.
Dogs take a really high dose of antihistamines compared to people, so don't let the amount worry you. They require more than we do per pound of body weight. This may make him a little sleepy.
You can also give him ice cubes to lick to soothe any throat soreness and allow you to see if he is having any difficulty swallowing.
And then you'll need to watch him closely for any progression of symptoms. That includes difficulty breathing, vomiting or diarrhea.
The effects of the sting should resolve slowly over the next 12 to 24 hours with antihistamine use.
In extreme allergic reactions they can get shocky and collapse but you should see difficulty breathing and vomiting/diarrhea first. Those types of severe reactions are very rare.
Most reactions are managed just fine with antihistamines alone.
If you notice progression of his symptoms don't wait, have him checked on an emergency basis.
If you'd like you can have a veterinarian check him now. They can give a cortisone injection which will lessen symptoms faster. But if he seems to be doing well then I would just use antihistamines and take a wait and see approach.
Please let me know if you have any further questions.