Is it normal to eat dead skin?
Depends.It depends
A little dead skin from your lips or fingers now and then isn’t unusual. Regularly seeking it out or feeling unable to stop is less common and may be worth paying attention to.
If you mean occasionally chewing a loose bit of skin from your lips or fingers, plenty of people do that without thinking much about it. It’s not exactly a dinner-party topic, but you’re not alone.
If you’re deliberately picking and eating skin often, or it’s causing sores, bleeding, or distress, that’s a different story. Try to notice what sets it off and keep your hands occupied; if it feels hard to control, you could bring it up with a healthcare professional without embarrassment.