Apple ID account change

I just got an iPhone 5s and switched my primary email on my Apple ID to a different one from the last one I had. Whenever I try to use the App Store or retrieve email from iCloud, it comes up with my old Apple ID and will not let me use my old password, nor any of my new ones with my new account, to sign in. It repeatedly comes up as "Cannot Get Mail: The user name of password for "iCloud" is incorrect." When I try to go into settings and fix it, it comes up with my old ID and the same thing happens. Help please?