This is based on slightly older versions of iTunes, but assuming they haven’t changed too much…
If you’ve already dragged all of your music into the iPod folder, try going to File > Add Folder to Library. Once you’ve done this for all of your music, it should show up under Music. When I do this to a large amount of files, I tend to do it in smaller chunks, so that there’s less risk that I have to interrupt the process while it’s in mid-transfer.
Also, be aware that if you sync your iPod with this computer, you will probably lose the files that were synched with your work computer. If you are using an external hard drive, and using it on both computers, you’ll need to tell iTunes where to look for your music, or it will simply copy all of your music into your C drive. To change the directory where iTunes finds your music, go to Edit > Preferences > Advanced, and under “iTunes Media folder location”, click Change to browse to your external hard drive.
If you are using an external hard drive, make sure you always plug it in before opening iTunes, or iTunes will sometimes switch the music back to your C drive, and try to create a new library based on that (even if you have nothing there). Or it will show you your songs, but not let you play them because it can’t “locate” them. It’s just one more thing you have to be mindful of.
Also, managing music on two separate computers means updating the library every time you switch, so be careful to add any new files to the library after switching – or these won’t show up in your music, and they’ll be removed from your iPod when you sync. In general, I find it’s a lot simpler to keep all music files on a single external hard drive, and sync my iPod with only one computer.