All my kids are intense, and I've gone through this kind of thing with two of the three. My oldest has, for the most part, grown out of it (she'll still have sobbing fits for a long time when things get too intense and one last thing seems to overwhelm her).
My middle child didn't really scream. He shut down - flopped on the floor and became totally unresponsive. He has had challenges with coping with emotions all along. In first grade his teacher suggested that it was everything from aspergers to a seizure disorder (I've talked with the doc and it's neither!) He is emotionally really immature. I just have had to take it one day at a time. Usually when he shuts down, I make sure he's in a safe place and then I ignore him and go on with my life. When he's ready, he gets up and joins us again. He's been getting better, so lately (the last 6 months or so) I've been able to encourage him to "be a big boy," or to impose consequences - "you need to get up and do this or you can't play computer today" and it's been working. But for a long time it didn't and I just had to leave him alone. The more attention you put into a behavior the more it is likely to happen. So when your son has a screaming fit, I would close him in his room (been there, done that too) and leave him until he is ready to calm down. It's okay to check on him but don't give him a lot of attention while he's screaming. Do give him the attention when he is calming down. You also may be able to talk with him when things are calm and help him come up with other strategies of dealing with his frustration. (He won't be able to implement them on his own at first, but keep working through the process).
There's a good chance he will grow out of this. My son is 8 1/2 and, although he is still emotionally behind other kids his age, has made HUGE improvements, especially once I realized he wasn't trying to be naughty and I just had to treat him a little differently than I did my other kids. Focus on giving your son what he needs right now, and don't worry about being "fair" between him and your daughter; give them each what they need and that is more fair than treating them the same.
If he is still having challenges the next time you see the doctor (before he goes to Kindergarten), discuss it with the doctor. Give him specific examples of what happens and get his input on what to do next.
Hang in there! It's hard to see the other side when your in the middle of it, but as he gets older you'll be able to see that you did the right thing. Focus on what he's good at, and enjoy the ride :)