Have you checked here Apple ID: Your Account for Everything Apple https://appleid.apple.com/#!&page=signin to see if it is turned on under your new Apple ID? Maybe you can turn it off if your new Apple ID has not bee effective for more than two weeks. See:
Two-factor authentication for Apple https://support.apple.com/en-us/HT204915 and more specifically the section entitled Can I turn off two-factor authentication after I’ve turned it on? "You can't turn it off unless you recently updated your account. In this case, you can unenroll within two weeks of enrollment." But, I am not sure that changing your Apple ID is updating your account. Maybe not.
If you are in the two-week period, "Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure."