Ice.

Can you take aspirin? If so, put an aspirin in a piece of wet papertowel and place on the site. (Aspirin is taken directly into the skin and will help with swelling and pain.)

A wet tea bag (not decaf) can have similar pain relief (it's the tannin.)

I assume there's no stinger in the skin... it you didn't see it, how are you sure it's a hornet sting?
Fire ants, spiders, mosquitoes etc...

I think your doctor was insensitive. He should have given you a shot of cortizone or suggested what measures to take for this. Call an allergist and ask for advice over the phone. Being allergic to stings is a serious matter. Each time you are stung it can help you to become less allergic to that insect, or might kill you. Usually you know within 30 seconds which way it will go, if you are sensitive.

Glad you're still around! However, swelling is not good for the body, especially if it does impeded blood flood.

Get help.