Hello ruchelk,
Thank you for using Apple Support Communities.
If all of your music isn't being authorized on your computer, it is possible that the music was purchased under multiple Apple IDs. See this:
I have purchased music, apps, or books with multiple Apple IDs. How can I get all of this content onto my iOS device?
First, copy all of your purchased content so that it's on the same Mac or PC with iTunes. This computer should be the one you sync your device with.
iTunes for Mac: How to copy purchases between computers
iTunes for Windows: How to copy purchases between computers
Next, authorize your computer to play content with each Apple ID in iTunes. After your computer is authorized for all of your content, it can be synced to your iPhone, iPad, or iPod touch.
From the following article:
Set up your Apple ID for iCloud and iTunes - Apple Support
Regards,
Jeff D.