C.C.
I hate to disagree with the other mom who responded, but I don't think that is normal. At 16 months your son should be able to occupy himself. Have you tried putting him in a playpen? Of course by now he is a little old to train, and he might even be able to climb out. He shouldn't feel insecure since you are with him so much - but that might be part of the problem too. I do agree with the other mom that maybe part time daycare might be the solution - at least temporarily. Do you have any friends with children similar ages? Maybe you could take turns taking care of each other's kids - you keep them one afternoon and she keeps them one afternoon.
I raised two boys and now have two grandkids, and they all would play alone at that age - sometimes for hours! Mostly they would wander into the room I was in and "check" on me, then go back to whatever they were doing. My sister, however, had a son just like yours. But the difference was she NEVER left her son with anyone, she was with him ALL the time. And he became overly attached, just like your son is.
You NEED your time away, or alone, or at least time to get your work done! Do whatever it takes to make sure you get it!