MissDinSC,
That definitely helps clarify what you're experiencing. You mentioned that you can see those songs, can you also play the songs that you imported from CDs into your music library? In other words, if you select one of the songs that is being excluded from shuffle, are you able to play it successfully outside of shuffle?
Another thing we want to look into is the possibility that the songs you're referring to were marked as songs you want to prevent from playing. This may have been done inadvertently so it's a good idea to double check. This would need to be done on a computer, using either iTunes on a Windows PC or Music on a Mac. We're going to include the steps for both devices below.
If you're using a Mac: Prevent a song from playing in Music on Mac - Apple Support
If you're using a Windows PC: Play songs in iTunes on PC - Apple Support
You would just want to follow the steps in that article to check and see if the affected songs are marked as songs to skip and if they are, to click the check mark next to those songs to remove that designation.
We hope this helps!
Best wishes.