Two factor authentication is causing a problem with ITunes

Since two factor authentication has been turned on, I can no longer download music from ITunes. I try to buy a song and a code pops up on my phone which is fine, except there is no place on ITunes where I can enter this code, the song I am trying to buy greys out and won't let me do anything else to it.... I suspect this is because my laptop is too old and isn't running up to date software - and the pop up box which I assume should be appearing is not.... I have tried to turn off two factor authentication, but I can't - this is the message on Apples website:-

If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information. If you recently updated your account, however, you can unenroll for a period of two weeks. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require a higher level of security.

So basically, until I can afford to buy a new laptop (not happening any time soon!) I can no longer purchase music from ITunes?????? Fabulous

Any ideas?