THIS WAS EXACTLY WHAT HAPPENED TO ME when I had EDNOS!!!! I used that exact same technique, because "vomiting" was more like regurgitation that I would sometimes do unconsciously. I would hide the cups under my bed until midnight and then go when my family was asleep to tip them down the toilet. And yes people would think I just loved drinking tea. Ughhhhh. So disgusting. But eating disorders make you a pro at hiding what you're experiencing. I'm so fucking glad I'm recovered now. That was one of the worst times of my life.
To anyone with an ED who may be reading this - recovery IS possible! It truly is! I am completely symptom free now and have been for months. It took therapy and developing mindfulness, but it worked.