How do you soothe a fussy baby that wants to be held 24/7?

Have you tried swaddling? Swaddling reminds the baby of the womb. It gets pretty cramped in there. So a nice snug swaddle will do. Tune your radio to a static station the constant Shhhhhh noise is similar to the womb. And stop being so quiet around the baby, your womb is the nosiest place on earth. When it gets too quiet baby thinks its gone def. Also try filling a 2 Liter bottle with warm water wrapped in a towel and laying it next to baby (Use the back of your hand to determine warmth). One or all of these should help.