Screaming newborn; failure mommy

My baby is 4 days old and every night from midnight until about 2am she screams her head off. Nothing seems to soothe her. We feed, rock, swaddle, sing, snuggle, burp, and make sure diaper is clean. I'm at a loss. What else can I try? I think she is used to being active at that time because she was always moving then before she was born. But I just can't stand her screaming for that long. Is this normal? How long until she grows out of this? I'm feeling like a total loser of a mom because I can't even comfort my own baby.