I have a similar problem, although in my case "Shared" did originally appear, but then disapperared.
Home sharing from an iMac running OS X 10.7.4 to an iPhone 4S running iOS 5.1.1 was working with the iPhone connected to the iTunes library on the iMac.
Then the iPhone was taken on a weekend trip. However, it was still trying to access the iMac iTunes library, and there was no way to make it use its own Music library, because the "Shared" item in the "More" menu had disappeared.
Closing down the Music app and restarting it did not help. Powering off and restarting the iPhone did not help. Doing a hard reset on the iPhone did not help. This was very frustrating; no music all weekend…
When the iPhone was brought home at the end of the weekend, the connection to the iMac iTunes library went live, and music could be accessed.
However, there was still no "Shared" item on the "More" menu, so the iPhone could still not access its own Music library.
Eventually, after turning off home sharing on the iMac, the "Shared" menu item reappeared, and it was possible to set the iPhone to access its own Music library.
I have seen a wide variety of reports about the disappearing "Shared" menu item in posts going back 16 months to the "iPod" app. (This is now called the "Music" app, although much of the advice, including from Apple, on home sharing problems still refers to the iPod app, which is confusing a lot of people.)
Apple still seem unable to correct this faulty software, so why don't they make "Shared" a permanent "More" menu item, always showing the local Music library, instead of unsuccessfully trying to hide it when not needed? How bad would it be to always see "Shared" in the "More" menu even if only one library is available? I say a lot less bad than having the current mess…
If anyone has any insights, (beyond Apple's troubleshooting advice), into the problem described above, or other problems relating to the disappearing "Shared" menu item, please post!
Thanks!