I need advice about my old iTunes account and how to deal with iCloud
So I basically have an issue with my old iTunes account. I forgot to sign out of my old iTunes account on iCloud but used the same address and details on my newly created one. So now when I try to log out of my old one on iCloud it doesn't work. I remember the password but it just doesn't work. So then I went on the Internet to find the Apple ID and it came up with "Apple ID does not exist" so now I can't sign out because both my password and email at are wrong, and it's becoming a problem. I even called the Apple technical support and tried everything that I could possibly think off and nothing came out of it.
iPhone 6 Plus, iOS 9.2.1