Really starting to dislike my SO

My baby is 13 days old and honestly sometimes I feel like a single parent. I have to do literally everything for her. My SO got 2 weeks paternity leave and 9 days holiday to be off with me when she was born. I thought the whole point was for him to help me out those first few days and to build that bond with his daughter. 
He did nothing to help me out unless I started it first, at which he would get mad and tell me to sit down and stop making a point. He never wakes up to her through the night and if she does manage to wake him up he gets cranky and will just go off downstairs til I sort her out. He stopped changing nappies and will only do it if I ask. I had her on expressed milk for a few days and he would never offer to wash and sterilise them. He gets up in the morning and leaves me to try and sort DD, gather her bottles from the night, dirty nappies and her to carry downstairs by myself. She's 13 days old and he has been in the pub every day since her birth. He left me in the hospital on my own and came home to get drunk and has had the cheek ever since to complain EVERYDAY that he's tired! 
I had quite a few stitches so have to bathe or shower at least once a day to keep the area clean, but I hate having to leave her with him because he doesn't watch her and will play on FIFA instead. I have to rush so much because every time I get back down she's crying and he's not comforting her but playing his stupid game! He never comes anywhere with us unless it's his mums house, and probably only came with us to register her because he wouldn't be on the birth certificate otherwise. I'm getting so pissed off with him and if I try and say anything he says I'm "on my high horse and think I'm better than him" and he's "entitled to down time" but gets mad when I tell him to leave DD one when he comes in inebriated and stinking of smoke he goes straight to her crib and starts stroking her face and poking her cheeks! 
I think I'm gonna go down for murder before she's a month old! I honestly cannot wait for him to go back to work, at least then there's a valid reason as to why I have to do absolutely everything