What does it mean when you wake up with the bottom right part of your eyeball sore and twitchy?

Lubricate with drops: This needs to be worked up by your eye doctor for possible dryness or exposure during the night, and can be related to medical conditions that need further work up. That's the part of the eye that may not be fully covered while sleeping. So it smarts upon awakening. If so, it's simple to treat with otc lubricating drops that they can give you. But don't ignore this! protect your cornea.