To be "caught up" means you are thinking about something so much that you forget other things. It might be a pretty girl but it is usually used for some task at school or work, or watching tv, or surfing the web. example: " I got so caught up answering questions on italki that I forgot to go to class."

Imagine you're a fish, and you get caught up in a fishing net. This is where the expression comes from. The rest should be obvious.

To make up a deficit. Also to become involved in a situation. Usage of “caught up” After the trans-Pacific flight, it took one week to get caught up on my sleep. She got caught up in a drug trafficking ring. She now spots and reports police locations to the network. http://www.idiomquest.com/learn/idiom/caught-up/

This is Hurley of the Brian class speaking to classmate Rami: Attracted by some one or thing, like you facsinating a girl.