Tried to change Apple ID Password, now nothing works!

Hello,

Because of the new Password Auditor on macos Mojave, I decided to change my Apple ID Password to something stronger. However, this then prompted my iPhone to show 'Update Apple ID Settings - Some account services require you to sign in again' in Settings. However, the email that came up to endure the password for is my old Apple ID email. So when I enter my password, it just says 'Verification Failed. This Apple ID has been locked for security reasons. Visit iForgot to reset your account.'

I also tried signing out of my iCloud account my iPhone, but now when I try to sign back in, it just gets stuck forever on the 'Signing into iCloud account...' screen.

Any help would be greatly appreciated, as now all my iCloud features are disabled!