Why can't I install iOS 9.3?
Apple yanked iOS 9.3 (13E233) for almost all devices on 03/24/16 which means you can't install it. And no, you cannot force an update to iOS 9.3 since Apple is no longer signing it.

Update: iOS 9.3 (13E237) has been released on 03/28/16 for most devices, so you should be able to download the new firmware and install now. If you still can't install, you likely have one of the few devices that still don't have an updated version of iOS 9.3. You can check your device's signing status here.