Howdy Bpasters,
If I understand correctly, you have verified that Apps are on enabled for Spotlight searching, but they just do not appear when you search for something. I would start by quitting the Settings app on your phone:
iOS: Force an app to close
Double-click the Home button.
Swipe left or right until you have located the app you wish to close.
Swipe the app up to close it.
When you have done that Reset the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
If the issue persists, backup your device to iTunes and then restore it as a new device and verify that it works.
How to erase your iOS device and then set it up as a new device or restore it from backups
If it does, then restore your backup to either verify it still works and the software just needed reinstalled, or isolate the issue to the backup file itself.
Thank you for using Apple Support Communities.
Take care,
Sterling