Never nag in a irritated voice, he will switch off and only remember being criticised, not for what. It will get you absolutely nowhere
There are other far more effective psychological strategies but you will have to stop enabling him.
Start living as if you are a single mother already. So, sort yourself out and your baby and don't ask him to help you at all. But do not cook, clean or do any laundry or anything for him at all.
Keep very calm and sweet and always pleasant (even if you have to grit your teeth at this stage)
If he asks you why say pleasantly that working full time with a baby is harder than you thought.
Start emailing him real or made up times when he has to look after your baby but if you think he can't be trusted with that, make yourself and the baby unavailable for a weekend or evening or something and give him a list of chores that he needs to do in that time.
You can say that you are worried about post natal depression and possibly give him a leaflet about it (or leave it in a place he will find it).
When you come home, assess what, if any, he has achieved.
If he is truly cold and heartless he won't have bothered to do anything. If he has made an effort, praise him.
Your only hope of getting him to pitch in is by making yourself unavailable.
I would not trust a man who drinks to look after my baby so I would give him.all the cooking and cleaning jobs instead.
Basically treat him as an employee and keep the emotion out of it.
You will soon discover whether you would be better off in your own place.
Good luck!