Hornet stings contain poison, but it is usually quite small in amount.Unless you are allergic to wasp venom, the hornet's sting is not lethal. It would take about 500 hornet stings to kill a human child and 1000 to kill an adult. Also the hornet sting contains 5% acetylcholine. This is known to send pain signals to the brain. Hence the sting of a hornet is way more painful that that of a bee.
Let's talk of the remedies now:
Step 1: Get away from the hornet first. There may be more around or the same insect may return to bite you.
Step 2: Check for the stinger. This usually does not happen but the hornet may leave a stinger on you. Check for a black stinger. DO NOT use tweezers. They may send the stinger further inside and increase the chance of venom getting in you. Use a sharp object or the edge of a credit card to slowly graze out the stinger
Step 3 : Work on reducing the swelling and numbing the pain. An ice cube can be put to use here. Apply an ice pack or ice cube wrapped in a cloth. This reduces the swelling to a great extent.
DO remember that the pain might take a few hours to reduce. If you feel that the swelling or pain is too much then it is good to get to the emergency room.
Some more home remedies
A topical pain killer or pills like ibuprofen would work, but consult your physician before taking these.
A thick paste of baking soda applied on the sting/ swelling would reduce pain considerably.
Soak a small cloth in Apple cider vinegar or plain vinegar and apply to the sting until pain reduces.
The same thing can be done with lemon juice too
A freshly cut piece of potato, onion or cucumber held on to the sting reduces the pain
Olive oil can also be applied
Crushed parsley leaves applied topically also provide great relief
The next time some one around you gets stung by a hornet, you know what to do. Always remember to stay away from hives. It's better to be safe than sorry.