Howdy HBailey,
It sounds like the proximity sensor just suddenly stopped working when you updated to iOS 8.4 despite restarting and resetting the settings in the Settings app. Removing the case is where another step I would have done as well, so next I would quit all the running apps on the phone:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
If the issue persists then given the previous troubleshooting, I would next backup your device to iTunes and restore it as new 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.
If none of that works then I would have to recommend you seek service for the phone, but I don't think it should come to that:
iPhone Other Repair Options
CLOS