It could just be a learning curve. Don't cover him when he screams-- just wait it out and don't come back until he is quiet for a set period of time. Start low if it's really bad--- e.g., quiet for ten seconds....After screaming starts, wait for a break in the screams and start to count to 10 in your head (1 Mississippi, 2 Mississippi, 3 and so on) If your bird screams at all, the count starts over. Once you get to 10 and he hasn't screamed at all for that full 10 seconds, go in and praise him for getting quiet--- let him out etc. You don't want the screaming to be associated with any attention from you or let him think that by screaming, he gets let out (that is why the 10 seconds matters).
If you KNOW when he is about to scream, you can either let him out before he actually starts screaming, or try giving him a treat or something before the screaming starts (can't scream and eat at the same time).
It is possible that he is calling for you. Does he also scream if he is out of his cage but cannot see you? If so, same rules apply (excluding situations in which his safety would be compromised).
He will eventually figure out that screaming doesn't work to get your attention-- he's still going to do it some, but if you are consistent and wait him out every time, he's going to do it less over time. That having been said, it will likely get worse before it gets better, so make sure everyone knows that when he is screaming for attention/to get out that no one look at him/talk to him etc. Something as small as eye-contact is a form of attention and you don't want that.
Another thing you can do is practice leaving the room and returning JUST before the screaming starts, and praise for being quiet.
After a scream and ignore session, pick a key would to say about the behavior you like- e.g., thanks for getting quiet (said in a quiet voice yourself).
If he is screaming for you, another thing that can help is if you talk to him when you are out of the room (BEFORE the screaming starts--once it starts, ignore until you have 10 s of quiet).
If 10 seems impossible, you could try a shorter interval of around 6, but I wouldn't go below that. Over time, you would increase the number of quiet seconds before you return...so week one, maybe you do 6s, then week 2 maybe you do 8s and so on...I would try 10 and just expect to put up with a lot of screaming initially because he's going to make the behavior bigger before he decides it isn't working.
Macke's earplugs work better than those silly Styrofoam ones...
Also- have you taught him to play with his toys? They often have to be taught.