Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am very sorry to hear about poor Peanut's hornet sting paw.
Ideally we would remove the stinger to stop the toxin from being pumped in via the stinger, but I understand that she isn't cooperating.
Treatment is based upon stopping further allergic reaction by removing the stinger and then with antihistamines like Benadryl and sometimes cortisone if the reaction progresses.
Is her breathing and activity level normal?
Any vomiting or diarrhea?
Any difficulty breathing?
You can give her Benadryl (diphenhydramine only don't use the combination products with decongestants or acetaminophen as they can be toxic for dogs) at 1mg to 2mg per pound 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 will 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. This may make her a little sleepy.
You can also apply a cool compress to the worst areas and/or give her a cool water bath with an oatmeal based shampoo to soothe her skin. The cool water will close skin capillaries and reduce inflammation and oatmeal reduces inflammation. Lather gently, let it sit for several minutes and then rinse with cool water.
And then you'll need to watch her closely for any progression of symptoms. That includes difficulty breathing, vomiting or diarrhea.
The swelling/redness should resolve slowly over the next 12 to 24 hours.
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.
Because you know now that she has these types of reactions you should keep Benadryl on hand at all times.
If you notice progression of her symptoms don't wait, have her checked on an emergency basis.
If you'd like you can have an emergency veterinarian check her now. They can give a cortisone injection which will lessen symptoms faster. But if she seems to be doing well then I would just call them and let them know so it is on her record for future reference.
Please let me know if you have any further questions.