I can't change my security questions, so I am locked out of my account

See If you forgot the answers to your Apple ID security questions https://support.apple.com/en-us/HT201485

At this point, there is no way to change them without Apple's help.

You have indicated that you can't answer your security question satisfactorily. So see Security and your Apple ID https://support.apple.com/en-us/HT201303

This document says “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.”

Thus, given your indication, we can do nothing to help you, except to mention that Apple support might help you if you have an extenuating circumstance (e.g., you have your receipt for your purchase of a pertinent device from an authorized Apple seller with its serial number on it). If you want to contact Apple Support to discuss any possible extenuating circumstance, see the support options below. Alternatively, if an Apple Store is open in your area, then you can go there to deal with your extenuating circumstance. You also can make a genius-bar appointment (https://www.apple.com/retail/geniusbar/) if you want.

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple ID account security for country-specific and region-specific help https://support.apple.com/en-us/HT204169

Get Support: We’re here to help https://getsupport.apple.com/. Go through the options to find the best support option.

If you are being told there isn't enough information to reset them, contact Apple ID Support.

If you don't know the answers, if the steps in the article below don’t work, contact Apple ID Support, although I’m not sure they will be able to help. 

Apple ID - If you forgot the answers to your Apple ID security questions.      

From the 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 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. 

Apple Support schedule phone call

https://twitter.com/AppleSupport