It does not sound like your issue has anything to do with upgrading iCloud Drive. If you are signed into iCloud and Find My iPhone with an old ID, then it remains signed in until you sign it out.
If you simply changed that old email on your Apple account to the email you are using now, you can go back to: Apple - My Apple ID, sign in with your current email and password, and EDIT your email to be the old one. This is temporary, so do NOT validate the email address and do NOT change the password.
Sign out of Find My iPhone and then go back to: Apple - My Apple ID and change your ID back to your current one.
If it is a different Apple account altogether, then you need to click on the Forgot password on the Apple - My Apple ID link, and then answer the Security Questions for the old ID in order to change the password. If you cannot remember the password, then you will have to contact Apple Support to get a reset link: ACCOUNT SECURITY SUPPORT
Cheers,
GB