Is your partner helping, make sure that he realises this is his child too and that an equal share of household tasks and baby care should be on his shoulders.
Two other pieces of advise I was given when I went to the doctors with much the same complaint when my daughter was small. 1) does it really matter if the house isn't spotless, it's more important to spend time with the baby (is there any chance you could afford a cleaner just a couple of hours a week) and 2) no baby ever died from crying. That was the best one, as I spent half my time walking around comforting the baby, even though she was fed, bathed, changed and I could find nothing wrong just that she had me wrapped around her little finger.
Most importantly though I think you should get your partner on board, possibly work out some sort of rota for cleaning like you would for kids/pocketmoney and try to stick to it, a little every day from two people should keep on top of things.