Try logging out of the iTunes & App Store with the existing Apple ID on your iPhone followed by logging back in with the new Apple ID email address that was changed.
Settings > iTunes & App Store. Select the Apple ID and at the menu window that appears, select Sign Out.
Sign back in at the same location.
Did you change your existing Apple ID, or did you create a new Apple ID?
If changed, before changing it per the following link.
- Sign out of all Apple features and services that you use with your current Apple ID.
If you didn't sign out of all Apple features and services priior to changing your Apple ID, you may need to contact iTunes Store support.