I second this wholeheartedly. Please talk about these feelings with someone, and pursue a session with a mental health counselor if possible. Being a new nurse is extremely challenging and many of us have also gone through the awful cycle of eat-sleep-work-repeat; however, it definitely should not be allowed to take your desire to live your life.
It's easier said than done, but try to remember that it's not your problem if people are critical of you for asking for the help you need. You are new and need to ask questions! Also, is it possible that these two nurses were simply discussing a private matter because they are close, one that had nothing to do with you? Sometimes in the heat of the moment it feels like we are being judged more harshly than is actually the case.
As for the situations where you are asked to be three places at once and can't be, please try to be more patient with yourself, because that is an obviously unrealistic expectation. You will learn with time to prioritize and consolidate tasks and it will feel easier, but sometimes the to-do list doesn't end and some people have to wait. It sucks if they get annoyed with you, but just remember that you are doing everything you can. The size of your workload is not a verdict on how good of a nurse you are.
One thing that is helping me through a stressful time at work is determining what I expect of myself and what my limits are before I even get to work. A similar exercise may help you define what you need to strike a more ideal work/life balance. For example, I expect myself to:
keep my patients safe, try to meet their priorities, and advance their care
help my coworkers whenever possible and learn from them
ask for help and wait for it, rather than do anything I'm not properly trained to do (I'm in a new specialty area, so this has come up a couple times)
In exchange, I honor myself by prioritizing my tasks, taking a real lunch break (not always the full time, but enough to eat an actual meal), and not staying late. This is what I find I need to give my best to my patients and team, while still having energy to give myself on days off. I would suggest reflecting on the kind of care you want to give your patients, and what you need in order to do that consistently.
All the best to you! This is very hard work, especially in Peds (I would think), but it sounds like you are very conscientious and thoughtful - in other words, great nursing material. Hang in there.