Zara had no qualms about being carried, whether by Quinn or the other people who worked for her. After getting used to such treatment, she no longer felt that there was anything weird about it.
So, what if people saw her being treated that way? It wasn't like she could do otherwise and pretend that she was healthy and faring well.
At the moment, she was still sick and until she finished the mission, it would remain that way.
Although the spring water was currently keeping her alive, it was guaranteed that her life wouldn't be saved completely due to it.
Besides, she wanted to be somehow truthful to the people who had supported her and made her feel like she wasn't alone during the time she was constrained inside the house.
It wasn't about pity but being self-confident enough to show herself who she really was to the world. When she got better, she just hoped that everyone would be happy for her.