Advice on long term relationship w/ a baby

My husband and I have been together for over 7 years.. Married for over one. We had our first baby January of this year. He was the most loving and supporting husband during my pregnancy and labor.. It was effortless with him by my side. When we brought baby home we started arguing a little.. No more than normal.. But I'm pretty sure we were just very sleep deprived!! However.. The arguing has been getting worse... He has to have the last say and get in my face and raise his voice.. And I just block him out and shut up because it's not worth it.. But it's hard! We don't even talk about it after we argue. We have no communication skills right now. Tonight we laid our hands on each other.. Not forcefully.. But our 1 month old daughter was in the room and he wouldn't let me out of the room we were in. He basically just prevented me from leaving and I kept trying to shove him out of the way(I was not holding her when anything physical was happening). The whole argument started because I was upset at him because he has spent his time home on leave playing video games. Even on the days he is home.. I pull all of the weight. It escalated from there. I am bad about asking for help sometimes but I feel like he should step up on his own when it is obvious I need help...Chores, taking care of baby, buying groceries and supplies for her, etc. I am not a stay at home mom.. I go back to work very soon and I am just frustrated because I feel I'm going to be soooo overwhelmed when I go back and I'm simply just tired of it. Our argument got out of hand... But I am just concerned with how we are going to go forward from here.. Whatever that might mean..😢