My mother told me long ago to never use tweezers. The best way to get a stinger out is to use a plastic credit card. You scrape the card over the stinger and it eventually releases itself. Since this is on your eyelid, I would think your fingernail would work. I also recently read that as soon as you get a sting to put a penny on it. It takes the swelling down almost immediately. Why this happens, I can't remember, but I will search for that article and post it if I can find it. Squeezing usually pushes the stinger down in further.
Sorry it's before coffee for me. When you scrape make sure it's in the same direction.
http://www.snopes.com/medical/homecure/b...