There are a number of things that you can do to relieve the swelling and pain of the hornet stings. The best home remedy is to scrape a dull knife against the skin in the opposite direction of the sting. This would help in removal of the sting. Then dab ice on the skin to reduce pain and swelling. You can use topical creams like diphenhydramine hydrochloride on the area. For reducing allergic reaction around the sting area use a topical hydrocortisone cream.