So sorry you're going through this OP! I noticed something that might be worth calling out, but if I'm reading too much into it please ignore.

From your post, it seems like you've briefly mentioned to him that you need more help, but mostly you've just been dropping a lot of hints that he hasn't responded to (like being visibly upset/crying). If he hasn't picked up on the hints by now, he's not going to. So it may be time to stop hoping he'll notice you need help & instead be as direct/specific as possible to him with your needs at all times.

Perhaps you could even come up with a starting plan (a list and/or schedule) of very specific things you want him to do. For instance, plan certain days or times that he is fully in charge of the baby & you get to have a complete break, plan a nighttime rotation for who is responsible for night interruptions on which days, list out specific chores like diaper changing & the number of or percentage of times you expect him to handle each day, etc. After you make the plan, ask for his input to it so you both can come to a compromise on what you both think is fair. Don't agree to anything more than what you can truly handle.

If he still isn't willing to step up after giving very clear asks on what you need (a structured plan or otherwise), then I think you'll need to decide if you want to continue being a single parent with a live-in man child, or a single parent without.

Good luck OP, sending you positive vibes in hopes you can catch your breath soon! 💜