I suggest a sling as well. DD1 was exactly the same so with DD2 we kept her in a sling for the first 12 weeks or so except at night and she was much more settled. I used to also have a nap during the day with her on my bed. I would put pillows around her in the bed and then sleep with my hand resting on her tummy. We both got really good sleeps and I wasn't worried about her ending up with a pillow on her head or under the blankets or me squashing her.

Hope you have more luck