Part 1. How to Solve Apple Music Library Not Loading
Check Network Connection and Network Settings
Network is the most important factor that cause Apple Music library won't load.
If you are using cellular data network, you need to make sure you have a big enough data plan. Also, please make sure you don't exceed the daily data limitation and you can browse websites online. You can turn on & off "Airplane Mode" to reset the cellular data network if it doesn't work.
Finally, please check the Apple Music settings on your Android, iPhone. You can open Apple Music app > Click "Settings" > Click "Music" > Click "Cellular Data" to confirm cellular data is turned on and enable "Streaming" if you plan on streaming music using cellular data.
If you are using Wifi, you can try to switch it to another Wifi. Or sometimes switching it on and off will simply do the trick too.
Switch iCloud Music Library Off and On
iCloud Music Library is turned off by default. In order to load the entire music library, please make sure the iCloud is turned on from your source device and the destination device.
If the settings is already on, you can try to turn it off and on because sometimes glitches happen.
Also, please note when you try to turn on iCloud music library, usually it will prompt you the options if you want to "keep music" or "delete & replace". The latter option will wipe the entire local library and replace it with the new library from iCloud, so please pay close attention to it. You should choose to "keep music" on the source device and "delete & replace" on the destination device.
Reinstall iTunes or Apple Music App
After years of developing, iTunes has became such a bulky software and it runs extremely slow. If your Apple Music library not showing up on iTunes, it is a good idea to back up your media files and then reinstall iTunes to start over.
As for the Apple Music App, it usually works perfectly for iOS devices with frequent update. But for Android devices, it takes much longer to get an update and a lot of users has reported many problems such as not downloading songs, crashing, Apple Music skipping, not loading library, Apple Music library missing and so on.
In this case, the one thing you can try is to remove the app completely and redownload Apple Music for Android from Google Play.