You may use the publish/share process to create a file that you may upload to a web site, but I don't think that "live" streaming is possible
What version of Premiere Elements and on what computer operating system?
You can get "live streaming" video into Premiere Elements using Premiere Elements' Add Media/Webcam or WDM (described "Capture video from webcam or WDM compatible device".
But when it comes to getting the captured video to your web site, then it is upload the Timeline content of the saved file to the website. Premiere Elements 13/13.1 Publish+Share/Social Websites/ includes built in upload opportunities for the Timeline content files to Facebook, Vimeo, and YouTube. If you select Publish+Share/Private Web Album, then you are dealing with Adobe Revel and not a web site of your choice.
Please review and consider.
Add ON...One link on the topic before Premiere Elements 13/13.1
As for Premiere Elements 13/13.1