You didn't do anything wrong, but I think you will need to contact Amazon to get that resolved. Otherwise you probably won't be able to log in to change anything.
Continuing from their help pages I referenced earlier,
- ...
- Confirm your sign-in using an Amazon mobile app
- To ensure you receive these confirmation requests, make sure your Amazon app notifications are turned on
If you are using Amazon's iPhone app for example, you can probably authenticate from within that app.
If that is not an option for you, then continue with the remainder of that page:
"If you are not able to sign in to Amazon because you don’t have access to the email, mobile phone, or other device that we’ve asked you to use to confirm your sign-in, contact Customer Service for help restoring access."
To be clear though, you most definitely do not need to use an "authenticator app". You probably just need to alter your Amazon account's log in and security settings so that you can use some other means of authentication.