Venting but any tips appreciated

I’m to the point where I don’t know if I want to stay in the relationship because my fiancé has a great work ethic but that’s it. I’m basically taking care of a grown adult and child at home. If he’s not working he’s sleeping, gaming or on his phone. I work almost full time, am in college, take care of a 9 month old, 6 animals, the house, groceries, and his stuff (laundry, food,etc). I’m unable to work full time officially because he doesn’t want to be a stay at home dad and really only takes care of the child in brief intervals. I’m just to my wits end because he refuses to help with animals or around the house but refuses to rehome animals. I’m drained physically and mentally all the time. This is someone who if there is a hamper 1 ft away still throws the clothes on the floor or thinks he needs to be appreciated when he does a small amount of dish’s. Won’t feed or give water to animals even tho I mention that they are out of food 3 times in 1 hr, doesn’t clean poop because he doesn’t like too, forgets to put stuff of or close doors knowing the animals destroy things. When it comes to me needed peace for school work it’s a hassle to get him to watch the child. I have not gotten a decent 9-10hr sleep since the baby was 3 months old while he has or chooses to play video games all night and complains of being tired. If I get a nap it might be 2 hrs tops before the child’s crying and he comes in the room to wake me up. I could be leaving for work and he wants me to change the diaper because he may have changed 1 earlier and I will stare like seriously I change them all the time. On his days off he tries to pawn the child onto others. A father should spend time with a child. I also have medical issues that limits me carrying stuff or anything of that nature. I’ve asked for help before for stuff to not be done and I have to do everything in the end. I’ve tried to limit tv time to when I’m doing school or eating but he seems to think that’s bonding time to watch tv all day or have a tablet in reach which I don’t like because I’m trying to avoid a tablet child. I don’t know what to do anymore and want to cry or sleep and avoid the problems.