My son screams at night unless he is held close to me or my partner...

I am a new mom, and my baby is only 5.5 weeks old. He used to only make noise when he was hungry or needed to be changed, and it was just a tiny cry. Now, if we don't hold him all night, he screams all night. My concern is that I might fall asleep holding him and have something happen like suffocating him or him rolling off the bed! I've been awake most of the night since he was born, but I plan to go back to work soon, so I'm afraid I will be too tired at night to keep myself from endangering my boy. Any suggestions??