But YOU are the one who is suffering here not HIM so he doesn't get to decide who YOU talk to about it.
I understand his need for privacy but this concerns you so your needs are just as important.
It seems that too much is about keeping him happy. He doesn't got to set the rules about what medication you can take and who you can speak to. Not even that you must make his dinner which he isn't even grateful for. You have a young baby, its unreasonable of him to expect dinner on the table every night as well, particularly when you have told him how much you are struggling. And then he complains about it! This isn't the 1950s.
His comment about how other mums manage is ridiculous. Lots of other mums have help from their partners, mums and other family.
I only had my partner and i found it hard not having my mum. I imagine you do as well and you don't even have your partner. If anything its like he is trying to sabotage you.
I understand that you don't want to just give up but you can't do it alone. If he's not willing to change, and try, admit he is wrong then you won't be able to do that for him.
It might be that he will never think that he has to help in any way. He has said quite clearly that you should be doing it all as the woman, i can't see anything changing there.