Two-Factor Authentication - hung on 'approve this iPhone/macbook message'

Hi there! I've just set up Two-Factor Authentication via my Apple ID account and all was going well except now I'm stuck with a message in my iCloud system prefs that I need to update my Apple ID settings. When I try that I'm getting stuck on a spooling 'Approve this' message on both my iPhone and my MacBook Pro. I'm not getting any messages on my iPad to approve either of the two devices. Keychain is off on both. When I click on 'can't approve this iPhone' I'm getting the prompt to 'reset encrypted data', but ideally I don't want to lose anything. All help gratefully received!