Trying to move my itunes?

I just got a new laptop. My old computer doesn't belong to me and I have less than a year before I have to give it back but it has my iTunes on it. So I want to move all my iTunes files and such over to my laptop and remove it from my old computer since I can't keep it. How do I do this? I don't have an external hard drive or a flash drive with enough space to move it all, so I wanted to try and do it with a shared folder. I asked my brother for help, and he found that my iTunes folder is already shared, yet it doesn't show up on my laptop or something like that. I don't really know much about computers so I was confused about what he said and he didn't know what the problem was. Can anyone please help me? The file has a little hand under it which my brother said means it's shared, but I needed some kind of account or something??? The network setup wizard said it was unable to do it or something like that. So basically I'm extremely confused and I need to move my iTunes and pretty soon I won't be able to anymore. So thanks if you can help :) OH and PLEEEEEAAASEE don't say "just transfer your purchases" because I have hundreds of songs from websites and such other than iTunes. So yeah, thanks.