I'm at breaking point, but so is my relationship.

I’m really struggling and need advice because I feel like my relationship is falling apart. I’m 9 weeks postpartum, and while I understand the baby is my main responsibility during the day since my partner works full-time (from home), I feel like I’m carrying most of the mental load—chores, cooking, shopping, and cleaning. I just can’t keep up. Our baby has been really unsettled and cries for hours leading to her being overtired. She either misses naps or feeds due to he crying. We’re investigating the cause, but nothing I do seems to help when I feel like she is in pain (we did take her to A+E over the weekend). Meanwhile, my partner’s desk is in the living room, so I’m mostly confined to the bedroom all day. I try to get out for walks or relax when she naps, but it all builds up. My partner still makes time for himself—he goes to the gym (when he can), has weekly band practice, and socialises with friends once or twice a month. He’s also preparing for a tour and recording sessions. I’ve told him I feel resentful because he’s able to keep living his life, while I feel like I’ve given everything to the baby and the house. I feel empty. Last night, I came back late from my parents so he could have a baby-free evening. He played games and did some laundry, which I thanked him for. But this morning, our baby wouldn’t settle, and I felt overwhelmed. When I saw the wet laundry he left in a heap, I just lost it. I ended up crying on the kitchen floor, and it all escalated when he criticised me for not calling the doctor on time (something we’d agreed I’d do). I told him to leave me alone at that point. I don’t know what to do. He really isn't a bad partner and he does treat me well, but it's just built up to us almost hating eachother. I feel like I’m breaking, and so is our relationship. Has anyone been through something similar? How do I cope with this?