Night time problems

I have a newborn baby so I’m expecting to be up regularly to feed and settle them during the night. However I can never put them down as they constantly want to be held and only sleep on me. When I put them down in their crib they just cry until I pick them back up again. I have tried various soothing things before and after putting them down but nothing seems to work. This means that I am getting no sleep at all at night and I’m falling asleep while breastfeeding. I’m not sure how much longer I can go on with only a matter of minutes sleep each night. Does anyone have any advice about what to do when a newborn won’t stop crying as soon as they’re put in their own crib? We don’t do co-sleeping or CIO. Thank you.