If it's an older model (1st or 2nd gen), it can only be associated with one iTunes library at a time. If it's the current 4th gen shuffle (or 3rd gen), and it was set to Manually manage music, you should be able to add new content from a different iTunes library. If it was set up for automatic syncing (to your old iTunes library), you cannot add content from a different iTunes library, without replacing the existing content.
If there are songs that only exist on the shuffle (you don't have a backup), you can first "offload" the songs from the shufffle, add the song to your new iTunes library, and then re-sync your shuffle.
You cannot use iTunes to transfer song files from iPod to computer, except for songs purchased from the iTunes Store. However, there are third-party methods and utilities that can transfer from iPod to computer. If you do an Internet search on something like "ipod transfer," you should get some links.