if a song isn't available in apple music, have i lost it from my library

I stored all of my music, ancient stuff from CDs and newer things bought from Apple, in iTunes. Then I changed computer. Now a lot of that music, including things like "mixtapes" made for me years ago and including things like albums that still appear in Apple Music, are greyed out and can be neither downloaded nor played. Have I lost these things forever by trusting Apple? Or are they stored somewhere, waiting for me to dig them out somehow?