I had a very, very hard time after DS. It wasn't depression related, he was effing hard! Turned out he had colic, reflux, and food allergies. Are you nursing? If so, have you tried changing your diet? If you are formula feeding, have you tried switching formulas? Do you swaddle? There wasn't a chance DS would sleep (and he still slept badly) if he wasn't swaddled as tight as could be. Do you try the swing? Have you tried wearing her? Does she spit up tons? If so, has the doctor checked for reflux?
I'm trying to think of what all we went through before anything got any better. To be honest, when ds was born I could not wait to go back to work because it was 1000x easier than being screamed at by a baby all freaking day. Around 9ish months, he got quite a bit easier. He still slept badly (and still isn't a great sleeper) but he was happier and at least napped. I know how much it sucks, it will work out eventually.
It may also be worth it to talk to your doctor abotu your feelings, but if your baby really is just difficult, it couldn't be the issue. I knew it was depression with DD when she was super easy and I was exhausted all the time even though she slept, and I was cranky, snappy, and just kind of angry when she was easy.