It looks like a stye but it's not. It's located on the outside of my eyelid. It just appeared one day. It's hard like a bump on my skin. What is it?

Get it looked at. Without seeing the bump, it is difficult to say for sure but if it is kind of shiny and you can see the blood vessels in it you should see a dermatologist to make sure it isn't a basal cell carcinoma.
Bite? Not too many things just appear in 1 day, except for a bite. See what happens over next day or 2 and go to ophthalmologist if not better.