OP, as a new mother with chronic fatigue and chronic pain:
Get a mother's helper, at least 2-3 mornings a week. I have mine 4 mornings. I hand her the baby and go to bed and sleep. I would not survive without that time, even with an involved husband.
As others have said its not about who is more tired. It is about what you need. I've read your posts and I'm not quite sure why you can't just leave your baby with your husband even if he is crying. Your baby is safe with his dad. You don't need to step in. You need to let go when you get given a break.
I'd strongly encourage you to make time and energy for your hobby. You need to fill your cup with more than just sleep. Make sure you are still seeing friends (with or without baby). I find seeing friends and doing something fun gives me energy. Even if its just baby cinema on a Wednesday.
Go for a short walk every day and try and see some nature
Take your painkillers - being in pain will wipe you out. Taking the right painkillers will give you energy eventually. Talk to your GP if you need to change prescription.
You are sounding a bit burnt out. Can you talk to your health visitor or GP about how you are managing? It's hard having a baby and health issues. Also your hormones will be crashing al over the place. I had a terrible 2 weeks 12-14 weeks after giving birth where I was incredibly low. Your hormones take 2 full years to settle after childbirth.
It is an amazing and exhausting thing to carry and give birth to and care for a baby. Be kind to yourself xxx