iTunes sign in loop

I recently purchased an app on my iPhone and it is not showing up on my Mac. With this, I tried to log into my account on iTunes instead of the App Store, and now it won't let me sign into my iTunes. I type in the correct password, and when I press enter it just asks me to sign in again. It lets me log into my old account, but I want to sign into my new account because this is what I purchased my app on. Please help!!