Hey there rosegirlmom,
Thanks for reaching out to Apple Support Communities. We'll be happy to help with Apple Music album covers on your iPhone.
Since it sounds like this is affecting only the iPhone, (and not the computer, iPad, or iPod) let's focus on the iPhone itself. To start, let's sync the iPhone with iTunes again, and remove all music first. Once complete, you'll want to restart the iPhone and sync it to add the music again.
You can find those steps here: Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support
Sync or remove content using iTunes
1. Open iTunes and connect your device to your computer with a USB cable.
2. Click the device icon in the upper-left corner of the iTunes window. Learn what to do if you don't see the icon.
3. 
4. From the list under Settings on the left side of the iTunes window, click the type of content that you want to sync or remove.* To turn syncing on for a content type, select the checkbox next to Sync.
5. 
6. Select the checkbox next to each item that you want to sync.
7. Click the Apply button in the lower-right corner of the window. If syncing doesn't start automatically, click the Sync button.
* You can only sync your device with one iTunes library at a time. If you see a message that your device is synced with another iTunes library, your device was previously connected to another computer. If you click "Erase and Sync" in that message, all content of the selected type on your device will be erased and replaced with content from this computer.
If the same behavior occurs with the incorrect artwork, reach out to Apple to look into this further using: Get Support
Take care.