Newborn refusing to sleep

This is my 3rd baby but I need some major help. I had one good sleeper, the other one not so much but I think that was our fault as new parents. My 6 week old is fighting sleep and then when she falls asleep either wakes up immediately or only sleeps for 10 minutes. She will only fall asleep if nursing or in the carrier. Rocking doesnt work. We follow the natural sleep cycles- so we try to have her in a carrier or done her sleep routine 45 or 90 minutes after the time she woke up. If I try to lay her down she’ll either just lay there wide awake or scream. I’m about to call a sleep consultant but also wondering if anyone is going through the same thing. I am so exhausted and desperate for her to get the rest she needs. Oh did I mention that every moment she’s not nursing or sleeping she is screaming? I’ve already cut out dairy and soy. I just feel so helpless right now.