Am I wrong or him?

My fiance got super pissed because our baby started to fuss. He has to work in an hour and we had just tried to lay back down to sleep until he has to get up. We woke up to feed our baby. Well I got the baby to sleep and then he started fussing for a few minutes. I wanted to see if he would try to fall back asleep. Well my fiance gets up and storms out of the room with him to bounce him on the exercise ball (that's how we get home to sleep) and hes saying things like I have to work in the morning, you just let him fuss when I have to get sleep. I'm tired too. He thinks I can sleep through the day while hes at work but I cant. I have to clean the house feed and change our baby, bounce him to sleep, but also cook and take care of myself when the baby is sleeping otherwise I dont have time to do anything for myself, there is no time to take naps for me during the day. And another reason is I just cant sleep no matter how hard I try. I know he has to work but I also put the baby to sleep every night and get up to feed him whenever he wakes up. I feel like I'm doing everything. I usually wake up every morning at 4 am which is when baby is usually waking up and I go into my living room so my fiance can finish sleeping. He got up no problem this morning when baby needed to eat because he wanted to get on his new phone that he got last night and can spend an hour on that, but cant help me with the baby because he wants to sleep one more hour before work. I wasnt even mad about putting the baby back to sleep but he started saying stuff like I should be doing this and that because he has to work when I do it every night! I know it's stupid to fight over this. But why do I feel like a single parent right now? I try to do everything because I know hes working to provide for us, but god forbid I not do 1 thing he flips out because he doesnt feel like getting up to deal with it.