Baby won’t sleep unless on me or pillow

My baby is only a month old and unless it’s on me she doesn’t like sleeping anywhere else. I’ve tried the swing, the bassinet, just laying her on the bed and she either immediately starts screaming or will sleep for only 30 minutes and is back up. I feel awful because it’s just so obvious she’s overly tired and frustrated because she’s not getting enough sleep.

Only time she’ll sleep for an hour or longer is if she falls asleep with me holding her which is dangerous and not ideal. Or she’ll fall asleep is if I lay her on a pillow to sleep which still is dangerous. I just feel like I’m stuck, she needs her sleep but I don’t want to put her in any danger.