It sounds like there is a conditional access policy in place that is enforcing Authenticator login. If that is the case, there are two things you can do:
1.) Check if there are other administrators in your organization that aren't blocked yet. An administrator with access to the Azure portal can disable the policy that is impacting your sign-in. (In your case it sounds like everyone is locked out, so this may not be an option.)
2.) If none of the administrators in your organization can update the policy, submit a support request. Microsoft support can review and upon confirmation update the Conditional Access policies that are preventing access.
If you had only one admin on the tenant you could reach out to the Azure Data Protection team (866-807-5850) for this, but they will only unlock if you don't have another admin who can do this for you. Your best bet in this scenario will be to talk to support.