Ok, I'm out of good ideas, so I'll just bounce some random thoughts around and see if anything helps.
1) I'm not sure what the difference is, but Library and My Music are pretty much the same menu. If you have a My Music tab, see if Home Sharing is showing up there.
2) I did a little online searching, and found something about iTunes Steraming Music being disabled making the Library tab disapper if you don't have a local library. I can't find a setting like this, but I'm on iOS 10, so the setting may have disappeard or been changed.
3) iTunes on the computer has a Restrictions tab in Preferences. There's a Shared Library checkbox. I don't know if this has any effect on Home shareing, but make sure it's unchecked just to be sure.