Along the way, Wukong had told Judith he could make it to his room on his own. But after letting him go for only a moment and seeing him wobble, she decided against it and helped him all the way.
Entering another hallway, with doors on each corner. Judith and Wukong ensured they were as quiet as humanly possible, so as to avoid being seen by anyone. If it had just been Judith carrying the prince to his room, they could have concocted a very simple lie that he had eyes for Judith, and so...
But considering the fact that he was tattered and covered in dirt and blood, the best option would be to avoid prying eyes and questions that would follow.
From the hallway, making it to the door harboring the prince's room seemed like a daunting task. Most especially because they were trying to move as fast as they could while walking as slow and quietly as possible. But after a painstaking amount of time, they finally made it to his room.