I've had two screamers in my experience, though neither as intense as this guy seems to be. The first one was the family's favorite chick, a brooder-raised Red Partridge Orpington cockerel. He was always "extra" in all regards. We called him The Screamer when he was a baby. Screamed and complained for no reason, but was otherwise healthy. He outgrew the screaming at one point - not sure exactly when, but around the time he feathered out and started looking more like a chicken. He remained very vocal, just less annoying. He was certainly all there upstairs though, and more - he was the smartest of the bunch, first to figure out anything new, knew how to get his way and manipulate his humans. Grew up into a beautiful cockerel with a normal crow. Sadly, he died at 7 months old of fatty liver, because he was such a pig and just couldn't control himself around food
My second screamer was a barnyard mix pullet, raised by a broody outside with the flock. Her brothers were quiet and perfectly normal, but she shrieked all the time and for no reason. She'd be under her mama's warm fluffy butt, and STILL shriek! I could hear her across the yard and from inside the house with the windows closed. She was eating, drinking, pooping, and growing, just always complained about everything. And she was a total mama's girl. The other chicks would be dust bathing or whatever, and she'd be glued to her mama's butt refusing to do anything else, followed her everywhere. She got forcibly cured of her screaming when I rehomed her and her brothers at 1 month old. I don't know if it was the shock of the new environment, or if she just outgrew it, but she doesn't scream anymore. She's 3 months old now and looks and acts healthy.
This is just a sample size of 2 though. Doesn't prove anything. But it is very possible that the screaming is just some weird personality trait that doesn't have to mean anything is wrong. It might, or it might not. Give him another few weeks and see how he does. Hopefully he'll outgrow it, too!