Personally, I don't really like iTunes, so I use Radium (get it in the App store), but a quick search on "Internet radio players MacOS" brings up a lot of alternatives.
How are you trying to stream internet radio? Is it through your web browser, though iTunes or through a dedicated app?
If you've been trying to do it through your web browser I can't think of any reason why it shouldn't work but, given that it doesn't for you, your next route to try should be iTunes:
https://support.apple.com/kb/PH19478?locale=en_GB