One example of character vs self is in the movie Tangled when Rapunzel is crying over the fact that she feels bad for leaving the tower against her mothers wishes while also being happy she was able to explore the world.
It’s also seen in the grinch when he’s invited to the ball. He’s fighting with himself saying he wants to go while also thinking they don’t want him there. The idea comes back when he had to ruin christmas, he argues with himself after meeting Cindy Loo Who and seeing the good in the world.
Character Vs Self is essentially just inner monologue of a character being frustrated with themselves and trying to come up with a solution.