Happened to my active little boy around the same time (3 or 4 months old) I was lucky because it was a quick fix for us. We just took out the baby head stabalizer (poofy thing that kept head in place) in the carseat because it was getting too small for him and he hated feeling his head squished. It was ok because by then he had control of his neck and head so he was wanting to look around. As for setting him down in a infant seat, do you feel like you have sat down to play with him several times during the day or do you mostly drop him in the play yard with a toy or leaving him in an Exersaucer while you start dinner? If so, he may feel that being held is the only way to get your attention. Obviously, you have to set him down to get things done but he first needs to feel he's getting enough comfort and attention in other ways besides using mom as a taxi. :)
*make sure all basic needs are met (wet diaper, hunger, too cold, etc.)
*Play with him on the floor on his tummy several times a day. As he learns new skills on his tummy, (scooting and crawling, etc.) he'll be better about exploring and entertaining himself.
*bring out some new toys (he'll love shiny mixing bowls with a rubber spatula, measuring cups, etc.)
*have two or three toys in reach but not too many, he'll get overwhelmed.
*Try change of scenery, try letting him explore in your bedroom or play in the infant seat in a bathroom or in front of a mirror.
*if these don't work, set him down, play with him for a few moments to distract him, then casually get up and go do what you need to do but be in earshot and maybe play peekabo around the corner or sing to him. Come back to reassure him often if he cries but don't pick him up. You can eventually leave him longer and longer periods with this.
Hope this helps.