Ahhh I'm sorry you going though this and so many emotions. It's so difficult it really is, it's so much we go though that it can feel like you have changed ten times a day. For what it's worth it gets better, because they do eventually sleep longer. I remember that newborn sleep depravation, I was getting 2-3 hours a day and felt like I was fighting to be awake.
My boy eventually went done for one slept in the night, and it's heaven to get a little sleep.
Im sitting here with a 16 week old who I just got into a nap. It's very normal, some newborns don't want to be put down, mine is 16 weeks now and I still can't put him down during the day. My heart breaks too much to hear him cry as well.
Might not be useful, but I coped by using slings, I also have an ergo baby carrier. As a newborn I could swaddle him and put him in the pram that stayed with me, but it was very short time Maybe gave me ten min, five at times.
My house work hardly ever gets done still, I just prioritise the musts first. I'm so OCD and I've had to just let it go. I don't pee alone, I don't put on makeup daily on the odd day fine. I am getting a gym workout from holding him, walking around swaying him.
The emotions in the first month balanced, and I love it. I love every single moment, once I realised he wasn't a newborn anymore, it hit so hard how short time is. It's for just a moment, and this is that moments of a lifetime. I embraced and love it, doesn't mean it's not hard. I'm sitting in a dim room, listening to white noise as I have a very sentivie baby.
I also didn't have support, family friends too far. We can't afford help. My partner helps, but as well he got to work, and had to work during his paternity leave too. I was doing the laundry four days after having mg baby.
Try embracing carrying them, and read a book. Find a series use headphone, try music. Ask your DH when he is arojnd if you need extra time and support.
And take photos, capture th moments, weather you look dressed up or not. Just enjoy the moments it goes so fast. I'm sorry if that's not useful, but u hope you find a way to cope for yourself.