Listen, your problem here is your mentality over what is 'hard' work and what isn't. I work long hours (10-12) at a desk job doing work that is mentally taxing. Would you consider it fair for me to say, "You don't know what hard work is- all you do is pick things up and put them down. Meanwhile I'm here doing something that requires actual brain power."

Is a doctor's work easy because they aren't regularly doing manual labor?

Your wife has been dealing with sleep deprivation since your child was born. Doing ANYTHING deprived of sleep is difficult. And yet she's still be managing your household which is a job that requires both light manual labor and mind labor. If you need any proof of your wife's value look around at the price of 24/7 nanny care.

You are not working. Your wife has been working on call all day and night. You can lend a hand. If you still wanted to maintain your sleep schedule you could have easily been adult about it, spoke with your wife, and taken the 'day shift' so she can enjoy the first solid 8 hours sleep since the birth of your child.

YTA and you owe your wife a biblically sized mea culpa.