Most people are aware that things can get stuck in their eyes. What they usually don't know is that apart from dust and eyelashes, even small bugs can get stuck in there.
This is actually a relatively common occurrence if you go biking through the woods without any glasses on.
Of course not every bug that hits your eye will get stuck in there. Regardless of if it goes in or not, your eye will be irritated for a couple minutes. Even if the irritation goes away, you're not exactly safe yet.
The way to tell if a bugs in your eye (without a mirror or a friend) is to lightly apply pressure along your upper and lower eyelid. If it hurts in any area, you most likely have a bug in your eye. The other method, using a mirror, would be pulling on the skin around your eye to see if there's anything under. A cellphone camera works just as well.
There are may ways you can attempt to remove a foreign object from your eye, but the one that always works is pouring water on your eye. Just be really really gentle and try to keep your eye open.
PS: nothing can get behind your eyeball otherwise contacts would be really dangerous