Fussy Baby

Last night and this morning, my newborn (1 week) was so incredibly fussy. She's been up all throughout the night. I just got her laid down (8am) after being up since 1 am. I tried everything I knew to soothe / calm her, nothing at all worked. I would finally get her to sleep and try to lay her in her bassinet, she would wake up and start screaming at the top of her lungs until I picked her up again. She did this several times. Even after I nursed, changed and swaddled her, she would still scream. I tried letting her cry it out , but it's like she wouldn't stop at all. I'm so sleepy... What do I do in situations like this?? Her daddy hasn't slept either, and he had to work today. The screaming keeps him up at night..... I need help!!! (First time mom) Thanks.