How to unlock my Apple ID even after changing my password

Have you forgotten your Apple ID?, Check your Apple ID via your email box, see this Apple article: If you forgot your Apple ID

If you forgot your Apple ID email address or phone number - Apple Support                  

OR see -> Having trouble signing in?

https://iforgot.apple.com/password/verify/appleid

after changing my password

Then this Apple article: What to do after you change your Apple ID or password

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.   -

Apple on Twitter        

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.      *