Did yo just change the mail address for your Apple ID, or did you create a completely new Apple ID?
Change your Apple ID - Apple Support
If you did create a new Apple ID, you'll have to deactivate the Activation Lock, before you can set up the phone again.
Turn off Find My iPhone Activation Lock - Apple Support
Also sign out of all Apple Services, before you set it up with the new Apple ID
What to do after you change your Apple ID or password - Apple Support
If you can't receive the verification code on your device, you can choose or add another trusted number or address to send it to. Go to the Apple ID page to make the changes for that:
About two-step verification and SMS - Apple Support