Baby won't stop crying

My 3 week old cries every time I put him down. I've tried his swing, his bassinet, crib etc. Unless he's being held he just screams. Nights are tough and so is the day time because it's impossible to put him down.

I've tried letting him cry for a few minutes to see if he would soothe himself and he just cries harder the longer I leave him.

Any suggestions? I can't get anything done!