I posted on your other thread - is he an academic? There are of course caring, lovely academic men, but the demands of the job mean that usually those who are successful have a partner doing the legwork at home, or else there needs to be a good level of understanding of co-operation for both partners to flourish. You are starting from a position of inequality, as he has already failed to recognise your own aspirations and support you to complete your own Masters, and without that understanding and co-operation.
My XH was (still is) an academic, and we are separated, and I would describe the way our relationship ended up as abusive, so you need to read anything I say through that lens. I never had a lie in in the six years we were together; in fact, he de-camped from our bedroom when DS was born. It is a massive issue because you are no doubt exhausted from looking after a baby, who may or may not still be night-waking, and he is not respecting that you have needs to rest.
This does not bode well for your return to work, I am afraid, as you will be in the position of having to get back into the swing of things at your own job, settle your baby into childcare and still presumably function on less rest than him; it is not clear from your post that you have much support/agreement on how things will work domestically, and if he is always off doing things at work, and sees his job as more important, you are on a sticky wicket already for getting him to pull his weight at home.
Sex: of course you don't want sex because it means more time that you don't sleep!! As I said on your other thread, sex becomes about more taking, rather than a reciprocal act of intimacy.
I personally would go to friends or family who you trust - you do not need to go into details, just that things are a bit difficult, you don't want to separate, but you need some space for a night or two. Good friends or family will be able to look after baby a bit so you can rest. (And sometimes, it actually does help to talk over difficulties with someone else in RL who knows you both; equally you can say, do you mind if we don't talk about my home life at the moment, there is nothing serious to worry about, I am just wanting a bit of time to be somewhere else?).
How long have you got before you need to go back to work?