I use a wet wash cloth I put in the microwave for about 5 sec. It take the swelling down. Use a bowl with a little bit of water in the bottom.this is to keep the cloth from catching fire. And make sure that your hands are cleaned if you have to touch it.
For a stye, use clean cloth and rinse as often as you can. You can also buy a special polysporin for eyes. But it may sting. Also, eye drops to help keep eye flushed out