This question needs to be split into two sections:
The goal of the Rookie Awards is to share your best work to a panel of industry professionals. This contest is not about creating new projects, it's about sharing what you have already created. With this in mind, if you have created a project for another contest, you most certainly can submit it as part of your Rookie Awards entry.
Any work that you have created, no matter where it was shared first, can be included in your Rookie Awards entry.
All other contests on The Rookies platform are designed based. You are given a brief to create something. In this scenario, you are not allowed to upload work you previously created.