I feel terrible.

I feel like such a terrible mother. I want to cry and just don't know what to do. It is 230am and baby will NOT fall asleep. She has been changed multiple times. Fed multiple times. We've tried her rocker and her basinet. Swaddled and unswaddled. I'm frustrated and like "what do you want child?!" and my husband is like "she's just a baby!" and that makes me feel absolutely terrible because I shouldn't be frustrated that my 6 wk old daughter won't sleep and keeps crying and fussing and grunting even though there is nothing wrong. 
But I've had so little sleep the last few days. I'm battling some borderline depression i think due to lack of sleep. I have no one to talk to, no friends who care. My husband helps as best as he can but he hasn't had to deal with her continual fussing and spitting up and millions of diapers and hormones and csection pain and lack of sleep for the past 6 weeks. Because I try to be the one to get up with her since he has to work so he mostly sees it on weekends. And baby is all mixed up every weekend because we had a million graduation parties to go to so her sleep schedule is all messed up. And my stomach hurts so bad from stress and all the weird food at the parties. 
I'm just so bad at this mother thing. I don't deserve to be a mother since I'm frustrated with my baby. Probably don't deserve to be alive but who would feed her if I wasn't around. I just feel so awful. She will NOT sleep. I apparently don't deserve to sleep either. So I might as well stay up because I will either have to pump or feed her in a half hour if she won't sleep. 
Sorry for the rant. I feel so alone and so terrible. And this is a safe place to vent. Thank you for listening.