I felt just like you, and I have a lovely pregnancy and easy birth so I just couldn't understand why I was filled with pure dread and regret. I remember one night when she was around 3 weeks old and I couldn't settle her one night and I just put her in her cot, closed the door, went to the back door and had a cigarette and just cried my eyes out thinking 'what have I done'.
Like you, I cared for her, I protected her, I fed her, cleaned her, cuddled her and went through the motions but there was never that 'rush of love'. I eventually seen my GP and I did have PND, however, I refused to take any antidepressants (no idea why as I'm on them now and they were a life saver).
It took me about a good 5 years before I started to feel love for my daughter, and it happened so gradually, there wasn't a rush, just the more I got to know her, the more she could communicate and we could chat, the more I loved her.
She is 9 now and my absolute pride and joy, I feel loads of positive emotions when I look at her now and I would go through the shit all again for her. She is amazing and my best friend.
I remember being in your position and reading mumsnet and people would say, 'it doesn't last forever' and I used to think how is that helping me? It feels like forever. I used to wish my baby's life away, it'll be better when she's crawling, better when she's talking, better when she starts nursery.
I am not sure if it's PND for you, I'm not a doctor. But please speak to someone about this, you could get some meds to help? They literally changed my life and I kick myself for not taking them when first offered.
If you find yourself getting frustrated (which is normal by the way) you are fine to put baby down safe in cot/Moses basket etc and walk away and have a breather. Make sure partner is helping so you can nap/go for a bath/ a walk/ a coffee. Or do you have family that you can call upon just to come round so you can sleep for a bit?
Honestly I know exactly how you feel, I promise it passes. You will sleep again, you will get used to this new human that has suddenly appeared in your life, how you are feeling lots of ladies have felt and are feeling but it will pass and you will be okay. It's sad women aren't encouraged to talk about this more, sometimes, simply, there is just no 'rush of love'.