How to not take out my stress on my SO?

I have a newborn and breastfeeding and staying up all hours of the night has been taking its toll on me. I know it's taking a toll on my SO too, but I resent him because he doesn't have to do much since he doesn't have the boobs and that he can sleep most of the night and I end up being snappy with him. I know he tries to help when he can but I've just been so stressed and I don't mean to take it out on him. He'll try to comfort me by putting his hand on my leg and rubbing but I'll end up flinging his hand off me. I just don't want this to take a bad toll on our relationship. Any advice would be helpful. I feel bad about it on top of just feeling crappy in general and I don't want to keep it up . .