Daughter only sleeps on us

My daughter is 7 weeks old now and she still only will sleep on our chests. My husband, me and my mother have been taking shifts. If I put her down (fully asleep or drowsy) she immediately wakes up and cries. This happens swaddled or unswaddled. I have tried bassinet, crib, rock and play, nothing works. My pediatrician says to let her cry it out but I feel 7 weeks is too young for that. Even when I put her down to just make something to eat she will scream and scream. If I let her cry it out I dont think she would stop crying. I dont know what to do besides continue taking shifts.