You're both very tired. You have just had a baby. You were at breaking point and he said the wrong thing, even though he was trying to make things easier.
You reacted strongly because the sense of rejection from a crying baby is intense, as well as exhaustion and feeling overwhelmed and then in he walks and adds to all your negative emotions.
Remember that he has been listening to a crying baby too and was upset too. Crying babies do that to adults. They affect us deeply, viscerally.
He should have been more understanding towards you, but I wonder if deep down he was feeling fear that you, the central caring figure in baby's life, weren't coping and things could unravel. His 'pull yourself together' attitude was wrong - massively wrong in this instance- but I think he just wanted some order and strength at that moment when everyone was fraught and you and baby were both screaming. He'd have been better to have given you some encouragement and empathy at that point, but he didn't.
Your reaction was completely understandable in the circumstances. Unfortunately it confirmed his fears and set him off on a strategy of shaming you for your outburst.
This was intolerable to you in your heightened, desperate state and you felt a wave of anger towards him. In a way, you were defending what was left of your dignity. It just ended up being a bit horrible. I'm sure you don't normally grab and pinch faces like a frustrated toddler, but his attitude was just too much for you after all you've been through recently.
Take this as a sign that you are massively tired and need proper support before you get to this point in future.
Around 6 weeks, babies often go through a period of being very hungry and unsettled at night. It's normal and is related to growth. It will get easier if you carry on feeding on demand.
In the meantime, try not to get into a theme of blame and shame with your husband. You will get through this. Babies challenge every fibre of us and parents have to be kind to each other to get past the unreasonable times with them.