무서워 and 무서워라?
I recently learned that 무서워 meant "I'm scared". But as I was browsing to Youtube, I heard someone say it was 무서워라. Where did the 라 come from? Do they mean the same thing? Or is 무서워라 a playful way of saying "I'm scared"? (As the person saying 무서워라 was kidding around).

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Answer

I don't konw the situation in the video but 
adjective + '~아라/어라' or '~구나' is  exclamatory ending ,basically. 
The move is so scary.. 그 영화는  너무 무서워요.
What a  scary the movie is. 그 영화는 너무 무서워라 or 그 영화는 너무 무섭구나.
The flower is beautiful.    꽃이  아름다워요.
How beautiful the flower is 꽃이 아름다워라. or 꽃이 아름답구나.

cf) Verb + ' 어라/아라  ' means a command.

Answer

I think your understanding is correct. Esp, people usually say when they are not scared, but use it as a prank. :)