They don't have the same meaning. To show someone up is to reveal their faults, usually by demonstrating how much better you are at something than they are. This may embarrass the other person. But it does not mean that one gets embarrassed. It means another person acts in a way that causes you shame because you can not compare to the other person.
Say you think you are good at lifting weights and are trying to impress some girls by lifting 100 pounds. You struggle with it. Then I push you aside and lift 200 pounds easily. I have shown you up.
Now, one may "curl up" when one feels embarrassed. Like the little bug. It's used to describe one's reaction to being embarrassed. When my dad drove me to school in his bathrobe, I just wanted to curl up and die.
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