L.B.
My son did that a lot when he was younger, and you're right! It does drive you completely insane! I just let him go. I knew that absolutely nothing was wrong with him, so I'd put him in his room for a while, and let him belt it out. Soon after, he would calm down and I would explain to him that I was not abandoning him, just didn't want to hear "that mess". Trust me, it will get better. He soon understood that if he screamed like that, he would be left alone and ignored. You should not feel guilty- you are doing the right thing.