Depends on the worldly music. It can be unhealthy to listen to it all the time. Some of it is okay to listen to in moderation, but a lot of the lyrics focus on what your flesh wants, or what they think your flesh wants. Sex, romantic love, nihilism, drugs. I find most worldly music is about this kind of stuff, & so find it mostly unhelpful, discouraging, & depressing. Even the ones that are meant to put you in a good mood. But it really depends on the individual song. Not every song has to be about Jesus for it to be good (tho he is the author of the goodness). Post some here.
I’m guessing your flesh is fighting against you listening to Christian music. There’s definitely times when I just don’t feel like it, but often I find turning it on ends up being more benefical than what I was expecting. There’s a wide range of it. Hymns, more contemporary, uplifting, lyrics that are Christian but aren't designed to be churchy or worshipy. It doesn’t mean you give up ‘worldly’ music completely, just that you recognize there’s definitely music that Christians shouldn’t be listening to, especially all the time.
If you are struggling w/ listening to any kind of Christian music, & are finding problems w/ worldly music, is there other things you can find to listen to, I wonder......?