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It sounds like the Airdrop function is not showing up in the Control Center as expected.
I would recommend first quitting all the apps:
- 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.
From: iOS: Force an app to close
THEN restart the phone:
Restarting your iOS device
You may be prompted again after the restart, but if it happens more than once, I would then backup and restore the device to iTunes.
iOS: How to back up and restore your content