I live in NJ and just turned 18 so the laws should be exactly the same. The driving test I took to pass was at the DMV (as yours should have been) and directly after passing the road test I went inside and they took my picture and took all my information and made a valid NJ permit (which is basiclly just a regular drivers license but its verticle on the card not horizontal~ indicating your on a permit or a restricted license basiclly.) Then when you turn 18 you go back and get ride of the restricted license and get your legit one.
When you took your road test did you do anything after, you should have gotten it directly upon completion