Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.
Try a restart.
Restart your iPhone, iPad, or iPod touch
Try a forced restart.
Reset Device.
If necessary, contact Apple ID Support for assistance. See the Apple Support articles below for contact information.
Apple ID - Official Apple Support.
Contact Apple for help with Apple ID account security - Apple Support. (Link doesn’t always load)
Get Support Work through the screens to get a chat option. You may have to pick a slightly different problem.
Apple Support schedule phone call
If necessary, try Twitter
https://twitter.com/AppleSupport.
From the Apple Support article below.
Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.
Security and your Apple ID - Apple Support.