Music Home Sharing not visible in iOS 10
I hadn't actually opened the Music app since I upgraded to iOS 10, but I did so to see what I could find for this question. On the main screen, I immediately have a Home Sharing option, and tapping on it goes to a screen with my computer's name. See screenshot below.

I'd suggest logging out of Home Sharing on your iPhone, waiting 15 minutes, and logging back in. Also make sure you're running the latest version of iTunes (12.1.5.21 as of this writing).