I beg you to cut your losses now.
It doesn't get better. It usually gets worse. He is selfish, lazy, imature, disrepectful of your time, happy to let you do everything. You'll end up feeling like his mum, and losing all respect for, and attraction to, him.
You've told him your concerns. Not that you should have had to. As a grown man he ought to know what needs doing without being told. But you have told him, and he sulks (yuk, childish and manipulative) then does nothing about it (so doesn't care / can't be arsed).
He has no respect for your feelings, your concerns, the fact you have to work harder than him.
He is showing you who he is. I beg you not to ever have children with someone like this. You will get more and more resentful as you run around after children and a man child. You will become ever more exhausted.
It's deeply unattractive behaviour coming from a grown man. It's also deeply disrespectful. It will eventually kill your feelings for him.
And please be careful when discussing this with him (if you decide to, rather than dumping him which is what I think you should do). Remember that he isn't doing you any favours if he does housework. It isn't helping. He doesn't desesrve thanks or a medal. He is a grown adult who is responsible for the house just as you are. You share the load 50/50 (if you work the same hours; if one you works more hours then the other does more).
Sulking on its own would put me off him. Being lazy and selfish and thinking a woman's job is to run around after a man - YUK.