Hey there cassie1025,
From the details already provided, it shows pretty much all the different ways to share music.
One specific link we wanted to share again was this one if you're still trying to use SharePlay feature to share songs. This link provides details about the SharePlay feature that you mentioned in your original message: Use SharePlay to watch, listen, and play together in FaceTime on iPhone
The section 'Listen to music together during a FaceTime call' is the section you'll want to use when using SharePlay. Keep in mind that there are also the prerequisites listed to meet for all that want to listen to the same song, and sometimes even a subscription may be needed. Some content may not be available across different countries/regions. We recommend reviewing this article in full for more details about using SharePlay.
We wanted to also add to what's already been explained. If you wanted to share music to a different app, you'll need to have an Apple Music subscription as per the requirements listed within this link: How to share music to Facebook, Instagram, or Snapchat on your iPhone, iPad, or Android device
If you're following all of the steps, and meeting the requirements for the different share features you'd like to use, we recommend letting Apple Support know what's been tried as they'll be in the best position to assist further: Get Support
Cheers!