feel like a failure

I think sleep deprivation is catching up with me. I've been trying to nap when my baby does but then feel guilt for not getting anything done around the house. He's been eating every 2 hours so not much time between to do much. My poor hubs has been working nonstop and now has to take care of grocery shopping, meals and any of the heavier house clean up as I'm recovering from a csection. I feel useless. And I feel like I'm not taking very good care of my baby. He eats gets his diaper changed and I try to cuddle with him but he's so heavy. I try to do a little tummy time everyday and read a book or something but I don't feel like it's enough. 
As for myself it's hard to just get a shower in and remind myself to eat something