OP please hang in there and focus on getting by each day. Having a difficult baby is REALLY REALLY CRAP and nobody can possibly relate unless they've been in that situation. Your baby sounds like it was born at a similar time to mine (late Dec) and spending the two ensuing wet, dark months with a shrieking infant nearly made me lose my mind. Going out for walks wasn't possible because she cried the entire time so I was indoors for almost two months with no sleep, house a complete mess and ear splitting screaming all day long. This was before the pandemic and I can't fathom how awful it must be now.
Even people who had babies in spring/summer can't really compare their experience since it makes a huge difference if you can pop outside quickly with sunshine on your face and hear the birds singing.
Going to be honest, things might get worse before it gets better and it's best to throw all expectations out the window. All you need to do is survive...eat when you can, nap when you can, only do the absolute bare necessities in the house and fuck it to everything else. Don't bother cooking if you can't find time, short naps are far more important. Bananas, nuts, cheese, crackers, toast, eggs, cereal, yoghurt, plain raw veg (not chopped in a salad), various frozen meals are quick and easy meals.
I wore the same outfit all the time and it was only washed if DD was sick on it. Same for hers...I didn't bother dressing her "for the day" and she was in pyjamas all the time, obv changed if there was poo or sick. I remember looking frantically on MN at the time when people would reassure you "it passes" but the thought of something passing at 8 weeks when you're stuck at 4 weeks felt impossible.
Newborns can't interact much because they have terrible eyesight and zero concentration. I did find that DD became a bit happier at 12 weeks when she could sit up and see things for herself. Just being able to get outside also made a huge difference, and I always used the car seat attachment on the pram chassis so she can sit upright to look at things. As soon as she was lying flat she would start crying again. The weather also made a big difference so please focus on that point in spring when the pandemic will be under control, millions will be vaccinated and you can leave the house for fresh air with your baby.