How do I transfer my iTunes library to an external HD?

My iMac was running out of space on the hard drive primarily due to iTunes (Music, Apps, Movies, etc) and photos. I just installed a WD My Passport 2 TB 3.0 External HD as an extra storage device for and chose to fill it with my music library. I watched a YouTube tutorial and basically just dragged and dropped my Music folder from the internal HD to the external. It took about an hour to copy--100GB worth of stuff but I think other files and programs got mixed in as well. Not all of my music is in the Music----->iTunes folder for some reason. Should it be?

Anyway, after it all copied and I made sure that it was on my external HD I deleted it from the internal drive and emptied the trash. The video said that upon startup of iTunes it would ask me what Library I wanted to open from--well, it didn't. It just opened on a few hundred songs that appear to be stored in the cloud (have no idea how those got there since I don't use the cloud). When I go into preferences=====> advanced, it shows that iTunes on the INTERNAL drive is the main folder. I can switch it to the external but that doesn't seem to make a difference.

I tried putting everything back on the internal drive and starting over, even rebooting from yesterday's Time Machine backup but it says that the disk is full. Any ideas? Thank you.