If your ID is locked you can't sign into your account to change the number. You need to change/add the number on your Apple ID. After the change, allow up to 24 hours for the change to sync. Before trying to make the change, sign out of Messages/FaceTime on all devices/computers.
See the Apple Support article(s) below.
If your Apple ID is locked or disabled - Apple Support.
If you have changed your ID or password, have you followed the steps in this article?
What to do after you change your Apple ID or password - Apple Support.
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
https://twitter.com/AppleSupport. People have posted it may take an hour or more to get a response.
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.