I published my media to a private channel and now I can see it on the front page, is it public?

No. Your media has the permissions of where you published it. If you can see your media on the front page in 'Most Recent' or another section, you can see it because you have permission. Other users who have permission to view it will also see it on the front page. Users without permissions to view the media will not even see the thumbnail on the front page.