Hello abwoitas,
Thank you for using Apple Support Communities. That's great to hear that you love Apple Music! I do too.
Based on your post, I see that before you switched to Apple Music you had about 500 songs on your iPhone SE. You can't get rid of these 500 songs on your iPhone because every time you plug your iPhone into your computer, it syncs to a saved playlist, which you can't delete. I know that it is very important to make sure that you can remove content from your iPhone that you no longer need. I'm happy to assist you with this.
You can remove this playlist, songs, and other items from your iTunes Library, while still keeping them on your computer. So, the next time you sync these items won't be added to your iPhone. Use the article iTunes 12 for Mac: Delete songs, playlists, or other items, specifically, this section:
Delete an item from your library
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Click the item to select it, and press the Delete key.
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Click Delete [item].
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Do one of the following:
Deleting an item from a playlist doesn’t remove it from your iTunes library or your computer. Deleting a playlist or folder doesn’t remove the songs in it from your library or computer. Deleting a folder removes all the playlists and folders inside that folder.
If you subscribe to Apple Music or iTunes Match, songs you delete from your iTunes library can still be available from iCloud, so you can play or download them any time.
If you can’t remove a song, make sure you didn’t select a song in a Smart Playlist with “Live updating” turned on.
Additionally, you can use the article Delete music, movies, apps, and other content from your iPhone, iPad, or iPod touch to learn how to delete or remove content from your iPhone, iPad, or iPod touch.
Enjoy your music!