I haven't read the other responses you have gotten yet, but I thought I'd tell you that we went through the same thing with our son (who is 2 and 1/2) right around the time he turned two. Maybe it's a growth spurt time in their lives, but we discovered that he was HUNGRY! He talks very well, but wouldn't ever ask for food or say he was hungry... just screaming and crying and doing the exact same thing. Asking for the other parent whenever one of us went in. Now, we make sure he has a bed time snack (even a "meal's worth") about 1/2 hour before we start the bed time routine. It has COMPLETELY stopped the screaming. Now he just wakes up around 7am and comes into my room, stands next to my bed and says, "Hi Mommy! I want some cheerios!" :-)
Maybe your little boy is feeling the same way? A little hungered? (btw, we have a 6 month old who shares a room, so I know what you mean about not wanting his screaming to wake the baby!)
Best wishes!
S.