Am I in the wrong?

So my baby is 5 months now and she’s just now barely starting sleeping better than usual, before now, nights were a nightmare, it’s easier when my husband isn’t working, but when he is working I’m literally the only one taking care of her until his days off again, she works nights 6 pm- 6 am and he leaves the house at 4:30 because he has to get there really early for some reason and he comes home sometime between 6:30 am-10 am depending on the day, sometimes he has to overtime, so most nights I’m literally getting no more than two hours of sleep, and mind you I’m running on these two hours until bedtime again, and even if i try to go to sleep as soon as I put my baby to sleep I will lay there for hours and cannot fall asleep, and I’ve tried all the breastfeeding safe methods I could to be able to fall asleep and I just can’t and I can’t take anything stronger, so I have barely enough energy to take care of my baby and only do dishes, that’s all I can do, so the house does get messy which bothers me so so much, so really I only have patience for my baby and I only have energy for my baby, and I count the minutes for my husband get home, and I’ve begged him over and over to not sign up for overtime but it’s so tough for me when I’m by myself and I still need him, anywayyyysss TODAY he tells me in the morning he signed up for overtime and the only time they tell you that you have to go to work is at 4:30, so basically at the last minute, and I was like why???? And he says it’s because we need money to save up for a house ( which we would’ve been saving up just fine if he didn’t buy things we didn’t need, like we’d go to Costco and waste a few hundred bucks 🙄) anyway, he said it’s only one day every pay period, which is every two weeks, meaning he might work 4 nights twice, or 5 nights all together, and I hate when he works 4 nightstand, because that means I’m with her 5 days because he sleeps through his first day off, so today he starts ironing his uniforms, all of them, and he only does that the first day he goes to work, so I honestly feel like he knew because other than that he just irons one, so baby’s fussy today and he’s not having it, he keeps complaining how she’s been tough, he’s great with her of course, but he basically isn’t handling it well and is begging for my help, I was busy at the moment but I stop what I was doing and took her, he hates putting her to sleep because he states it’s too hard so I’m always the one putting her to sleep, basically he only wants to be with her when she’s relaxing and she’s calm, but as soon as it gets a little hard he hands her off to me to deal with it, so he knows it’s hard!! He sees it, but today at 4:30, when I was getting dressed to go to the park he tells me he’s getting called in for overtime, like are you kidding me, so I was obviously upset, but I didn’t yell at him or anything, I just got undressed and took the baby and told him to go get ready, and he got mad at me for being upset, and he kept saying he won’t go if I don’t want him to but I know if I tell him not to he’s just gong to keep giving me attitude about it so I told him if he feels he has to then he can go, but he was still mad at me for being upset about it, he started ignoring me when he was getting ready and he didn’t even say bye when he left like seriously? You expect me to be cheery all the time no matter how sleep deprived I am but you can be well rested and still give me attitude and be mean to me and you’re mad at me for being upset that I have to be alone with her longer now? And he says it’s only one day BUT when he gets back tomorrow he’s going to sleep through the whole day and he’ll only help me at night when I have to wake him up, he’ll hear the baby crying but he won’t do anything unless I tell him too which I feel he should at least not make me feel guilty by waking him up at night but idk..... I told him that he can’t get mad at me for not having energy for him if he wants to work overtime