I changed my Apple ID and I am unable to update iCloud on my phone.

Welcome to the Apple community.

In order to change your Apple ID or password for your iCloud account on your iOS device, you need to delete the account from your iOS device first, then add it back using your updated details. (Settings > iCloud, scroll down and hit "Delete Account")

Providing you are simply updating your existing details and not changing to another account, when you delete your account, all the data that is synced with iCloud will also be deleted from the device (but not from iCloud), but will be synced back to your device when you login again.