Missing music in iPhone music library.

Hey there.

I’ve a few songs missing from my music library. When I search for them in the music app, they are there and I just press on them to listen to them, but I want them in my library to add to playlists etc. I don’t subscribe to Apple Music or iTunes Match etc so the “sync” option in the settings isn’t there. I’ve paid for these songs in iTunes so why aren’t they in my library? Does anyone know how I can get them in there without subscribing to yet another service just to listen to music i’ve already paid for? Thanks in advance for any help.