I was planning to answer, but then, as the conversation unfolded, I noticed other members had already answered, and each time, you added extra information to clarify the situation and explain that you had already done it or looked into it. There seems to be little left to add, and I fear what I meant to write will be of little help.
As someone else mentioned previously, and if you haven't done so already, my first guess was to suggest you look into Post Partum Depression. The lack of sleep you are experiencing might be a symptom of this condition or might be a factor that worsens the condition.
Finding help such as a nanny might also be of great help for everyone in the household, as you guessed.
Then, like another member said, every human is different and we must learn to navigate the situation, whether with ourselves or with our children. There has to be solutions to every situation, at least I hope so. Keep searching and look up specialists for you or for the baby, if needed. May it be behavioral, food and supplements, exercises, spending more time outdoors, etc.
Practicing daily good habits should help alleviate some of the "downs", such as being grateful, EE, gentle physical exercises (such as Qi Gong, Tai Chi, Gyrokinesis, Pilates, Yoga, aquaform), etc.
I too have my days when I'm pissed at Earth and Humanity in general. That it all sucks, knowing everything could be completely different (as in living in communities like in the movie Avatar for one example), and that most people are like Goldfish in a round bocal, not even realizing there is something outside their darn bowl. Then, when I compare myself with others, I start to envy what they have that I "lack" or "should be having" too! Such as having a nice house in the countryside, or a farm, instead of living in a shitty apartment. Which in turn makes me upset at my life for having made the "wrong" choice which placed me where I stand now. But then, I would not be the same if I had made different choices... So it's a mental hamster wheel, and I got bored with it, having suffered more than enough for decades, I stepped down from it and I'm now trying to climb off the fish bowl. But sometimes I go back to spin in the wheel for 5 min
A more personal share regarding babies: my daughter was an easy baby and my son was easy too, but when we came back from the hospital, he refused to sleep on his back in his Moise (he would not fall asleep at all unless placed on his belly). Plus the breastfeeding at night is a killer. So I found a great solution: I have a recliner sofa Lazyboy type, extra comfy and super padded, 2 pillows on each side for my arms, and loads of fluffy warm blankets. I slept in it for 3 weeks straight with my boy on my belly (skin to skin, belly to belly). When he woke up for breastfeeding, it was a matter of plugging him, and 10 min later we were both back to sleep with minimal disturbances. I can say I almost did not lack any sleep with him. I was able to gradually and slowly transition him to sleeping in a vibrating rocking baby seat, then in my bed, then in his bed.
He never accepted bottles either and I breastfed him until 2. He gradually waned by himself, and at some point, I stopped taking the milk producing pills, so there was nothing left to drink anyway.
Wishing you the best, hang in there
