I've been dealing with the same exact thing with my lone silkie chick. I have a clear plastic brooder in the living room. For a while, just being able to see me in the same room is enough to keep him/her happy. Then after a while its, "I NEED YOU!!!!" If I stick my hand in there, she calms down and starts pecking and making happy noises, but I can't spend the whole day with my hand in the brooder and as soon as I take it out she's back to screaming.
About 50% of the time I can tuck her in her "sleeping bag" (like a mother hen tucking her under her breast) and she goes right to sleep. But other times she just backs out screaming. I use a fluffy sock that's folded over on itself. When she goes in headfirst she can't see me leave, and since the sock surrounds her, she feels like "momma" is there.
I've spent way too much time handling her and I know I've spoiled her. Especially since she can see me when I'm in the room. She just screams until I pay attention. Luckily I have eggs due this week, so my only consolation is that she'll have buddies soon...if I didn't just jinx myself by saying that.
Try the sock. I don't know if they all have the tendency to want to burrow, but mine has from day one. Then at least she's in the dark and might get sleepy. Good luck!