It seems like you are wanting to be able to add friends in Apple Music but you aren't seeing an option to do so. Being able to share what you are listening to with your friends is nice. I'll be happy to provide some information on this. I'd like to make sure that you are running the latest iOS on your device. If you are not, please back up your device and then update it.
How to back up your iPhone, iPad, and iPod touch
Update your iPhone, iPad, or iPod touch
Once you have made sure to backup and update, then you should be able to use the following article to start sharing with friends:
See what friends are listening to in Apple Music
Let me know how things go and if you are able to start sharing.
Have a great weekend.