frustrated

My baby (he’s my first) is almost a month old and I’m struggling. Last night he was up literally all night, I didn’t get a single minute of sleep. My fiancé can’t take nights with him anymore nor can anyone else or he screams the entire night until I finally come take over. He will not sleep in a crib or bassinet or he screams until you pick him up, so I put him in a bed bassinet in my bed until that stopped working and now I just have to hold him all night. During the day it’s just as bad, I sat him down just to wash 1 bottle and he cried so hard he threw up, immediately stopped when I picked him up. I can’t even sit him down to eat or use the restroom, I haven’t eaten a meal in almost a week just about 1 snack a day if I’m lucky. I don’t even care about that anymore as I have no appetite at this point, maybe I’m depressed. No one can even hold him or he screams until I get him. I feel like a horrible mother because I got so angry last night and cried instead of trying to console him. I just feel so overstimulated, the sound of his cry triggers me at this point. I hate that I feel this way because I don’t want it to affect our bond and I know I’m his comfort. I just want to get away, I feel like I’m utterly failing at this. Please tell me I’m not alone. I’m open to any advice, I’m willing to do anything at this point. I love him so very much, I just feel like I can’t do it anymore.