I had this problem earlier but then knew how to fix it, it was when I sent songs to my iphone the cover art got messed up with art from songs I already have on my phone. I fixed this by uploading the covers on iTunes again but making them album covers then sending it to the iPhone but now I have the same problem but it wont let me fix it with the album art. It gets mixed with art from songs I already have on my phone. The art is correct on iTunes on my computer, but it's messed up on my phone, this has only happened with 3 of my songs and an album with 7 songs. I want to prevent it from doing it again. I have an iPhone 5s by the way, if that's needed.
I had the same problem. Twice... You will most probably have to remove and then re-sync your music.
Attach your iPhone and go to the music section. Remove the check mark to sync music. Your selections will stay intact for later re-sync. Sync your phone. When finished all music should be gone from the phone. Now re-check the mark for syncing music and do the sync.
This fixed the messed up covers for me.
I resolved the situation for myself... I quit Apple music and re-installed Spotify and it works like a charm!