My son, who is 21 months, has been doing similar things lately after an illness. He constantly wants to be picked up and held, or always be in my lap if I'm on the floor doing anything. If I don't pick him up he screams and cries. I think he is jealous of the other children and wants reassurance. I'm not sure what to do about it either... If it was a dck I would redirect or ignore but for my own son, I don't want to push him away.
I'm not sure what to do either so I can't help but I can certainly understand what you are dealing with!