feel like I'm on my own

My SO does literally nothing to help with our baby. Our baby is 7 weeks old now. He's never changed a nappy. He's fed him maybe twice, and that's being generous. He's never gotten up with him in the night even when he had 5 weeks off work.. If baby cries for longer than 2 minutes he can't deal with it and just hands him to me even if I'm asleep he will wake me up. When he comes home he expects all the housework to be done and he expects dinner on the table for when he walks in and if it's not then he nags until I start it. He doesn't do any housework himself at all. It's literally all down to me. Baby also has colic so it's non stop I haven't actually slept the last 3 nights and I doubt tonight will be any different. This is really getting me down because he sits there and moans he's tired and I'm like I haven't fucking slept since he was born what is your problem. When I asked him earlier if he wanted to hold Charlie while I was getting his bottles etc sterilised and ready for his next feed he literally went "no I'm too tired put him in his Moses basket" like I'm not fucking tired. I'm exhausted. I need some kind of support but I'm sure as hell not getting it from him. Whenever I bring it up though I get accused of calling him a bad dad so what the fuck does he want me to do. Also apparently I'm selfish for wanting my mom to have him overnight one night while I catch up on some sleep.