baby screams when put down

My 7 week old hates being put down. Every time I put him down he will start with a little wine which turns into a full blown screaming fit until I come pick him up. I can lay him down for maybe 20 minutes and as soon as he realizes I'm not there he wakes up and starts a fuss. As soon as I pick him up he stops or he immediately falls asleep. I need him to understand that it is okay to not be held every second. Ive tried the cry it out business and I can't take him screaming for 10-15 minutes. I've tried to put him down when he is drowsy, but he screams and wakes his self back up, at that point he refuses to be laid back down. I try talking to him when I put him down during the day to cook, clean, etc and I feel like that makes it worse. I already carry him in a wrap or a carrier most days, but I don't think that is healthy either. I really want him to start sleeping in his own bed. Right now he sleeps in my bed or laying on top of me, but it scares me keeping him in my bed as he gets bigger. My mom is going to be watching him over night soon while I go out of town for business and I'm scared all he is gonna do is scream. Any ideas what I can do?