iPhone requesting password for different Apple ID when updating apps after updating iOS
Solution 1:
The computer you used to upgrade iOS was apparently signed into a different Apple ID when you upgraded your device. The thing that doesn't make any sense is that the Apple ID signed in on the computer shouldn't matter - you should have to sign-in on the device with a a different Apple ID for it to matter.
That said, you can try signing out of the App Store on the device (App Store app > bottom of the Featured tab > tap on the button that says "Apple ID: xxxx@xxxx" > Sign Out), then sign back in with original Apple ID.