The 'Private' status simply means that your stream is not listed on the Shoutcast website, listeners can hear your stream from the URL that we provide (this can be customized in the control panel).
If you require a public server then you will need to upgrade to a Webcaster Plus account which will unlock extra features and benefits, including upgrading to SHOUTcast V2 which allows you to get listed on the Shoutcast website.