Oh my goodness those first mental days/weeks of having a new baby, particularly the first one, were for me, just so overwhelming, disorientating and exhausting. I felt completely out of my depth, had no idea what I was doing, and had never experienced tiredness like it...horrendous.
It's a shame actually that those very first days/weeks do pass in such a sleep-deprived blur as I remember very little detail about DS, I remember more crying, feeling depressed (undiagnosed PND I suspect), and so tired I could weep.
My OH was very good and helped a lot with the nighttimes. I was BFing but also added formula in fairly soon after birth as I was terrified he wasn't getting enough.
OH slept a lot in the spare room with the moses basket, would give DS a dream feed of expressed milk, and then settle him and bring him back into me when he next woke, when I would take over and have him for the rest of the night. This seemed to work for us, and I felt like we were sharing the tough bits as well as the amazing bits.
I recall vividly crawling into my bed a couple of days after his birth (which was traumatic - 28 hours, ventuse delivery, complicated, episiotomy etc..) sore, aching, tired and tearful, and just wanting everything to go away. I think had OH not let me have those moments, I may have cracked up altogether.
Having said all that, it's annoying to hear but it does get better, and I had another one 2 years later. She was (and still is) hard work, but you know more what to expect, and the sheer terror of it all isn't quite so bad.
Good luck OP..you'll get through it.