4 week old very won't let me put him down!

I have 2 other children, but they are 11 and 15 years old, I don't really remember having this problem with them...

My son is 4 weeks old and I feel like I can't do anything because he screams when I put him down for more than 10 minutes. I have tried the swing and bouncy seat and crib/bassinet...

I need to be able to shower and do laundry and eat, but I find it very difficult to impossible to do those things while he's screaming. I know he doesn't need anything because it's after I've fed him and changed him and he stops as soon as I pick him up.

I know there is all kinds of debate on letting them "cry it out" or if babies can be spoiled by being held too much...