Non existent sleep here too - it is awful and certainly changes my ability to cope and be sensible after a while. DH was not great at understanding and still struggles to 'get' how hard it is, mainly bc he doesn't do it.
Similarly the me time only happened after #2 was a bit older and I put my foot down.
I never said much to anyone else as it just made me feel worse, like I was a failure and DH was an insensitive twit.
Take care - the house work will be there when you feel up to it (never here ) and I learnt to do a few emergency meals for the freezer to take the pressure off days/weeks that challenge you.
Perhaps try to get some protected time when you are feeling better and more able to talk to DH. Even if it is one sleep in per fortnight/month whatever that means you are off duty. It is hard with little ones - and sometimes there are no easy/obvious answers. Sorry not much help -take care and one step at a time.