I definitely know what you mean about the screaming... It really wears on your nerves... If you come up with any solutions as to how to end the shrill, ear piercing screams let me know! My ds will be 2 next month, and he's been doing this same thing for quite awhile now. Some days it's not so bad, and some days it's ALL day long! He doesn't only do it when he's mad though. Also when he's excited, wanting attention like your lo (he also has a 2.5 mo brother), and for reasons I still can't figure out....
I can't get him to stay in a "time out", so I give him a warning, and if he continues to disobey, I put him in his room for a few minutes. This usually stops the behaviour for the time being, anyway. And it gives me a few minutes to collect myself, so I don't yell at him.
As for the diaper changes, we have JUST conqured this. He was doing the same thing as your lo, for I don't know how many months. I think he's about ready to be potty trained now, because he's being SUPER cooperative when it comes to having his diaper changed. He'll tell me he needs a change by either pointing to his bum, or getting a diaper, opening it up, and laying down on it. It's really cute!
So yes, it's a stage and it will pass eventually. Hang in there!