Kitty destroying my carpet. What do I do?

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Hello. Recently my kitten has been showing some odd behavior. She is an indoor cat, plays during the day and sleeps at night at the end of my bed. She goes to bed at aroound 8pm even if I'm awake or not, and then in the morning she wakes up at 3am-4am. After she wakes up the first thing she does is scratch on my door then I let her out and she goes to my moms room and starts meowing alot. If my mom doesn't open her door she goes back to my room and digs her claws into the carpet and she made a huge hole in the carpet that will need repair. I bought her a kitty scratch post and encouraged her to use it by putting cat nip on it, toys, etc. and she never does - she only sleeps in it. What should I do for my kitten to stop this behavior? Also, what should I do about my carpet? How can I fix it myself?