I picked up that you have had him for 2 weeks, and the screaming just started 2 days ago. So something has changed to trigger this; parrots don't scream for no reason ( even if it is a learned thing, the screaming starts for some initial reason). You've had Grey experience, so you know that anything can set them off. Look closely at what may have changed int he last several days. I would also consider having him thoroughly checked over by a qualified avian vet, who really knows parrots. A constant screaming issue does sound like its a pain related problem, as parrots rarely do anything 100% of the time whether its screaming, plucking, or other activity.
tick off things like
diet change
surroundings change
your appearance change
toy change
household members change
if he's near a window - has what he can see changed
new smell change
new sound change
Hope this helps. But really if he is comfortable enough to sleep on your shoulder already, he seems to have started to bond with you. If you can work thru this screaming thing, he might be an excellent companion.