How to change iCloud ID?
YES, you can change the email address associated with the Apple ID. The Apple ID is literally the email address (don't pay attention to the previous answer...)! It sounds like you created an ADDITIONAL Apple ID instead of updating the email address on your current Apple ID. 

Navigate to appleid.apple.com and login with your 'old' Apple ID email address, from here you will be able to update to your new email. However, you would also need to follow this process to login to appleid.apple.com with the NEW address and assign this a "dummy" email address so that you can assign the "new" email to your current Apple ID so that you retain all purchases and content associated with your iCloud account.