It won’t let me sign into my iTunes

Do you get a message to review your account information?

If so, when you get that message on your screen, tap Review to sign in, then review your account information.

Click Review repeatedly. 

Some people have only had a response after a second or subsequent click.

Try to download a free app at the App Store.

For example try to download this (is an free app).

Log in at appleid.apple.com and make sure you have payment information stored there.