1 year old with an extreme scream

My 1 year old has the most unnerving scream you could ever imagine. He has since birth where his baby crying was very high pitched, now moving into a toddler stage he uses it when he wants to get his way or wants to get attention or picked up. It is so unnerving it sends both me and my husband into fight or flight mode. I find it very hard to discipline him because of how stubborn he is and the scream just overcomes you, you just break and give in. Has anyone else experienced this? I would love some tips. I have a 2 year old who was more physical than loud, he would kick and hit and eventually my sternness with time out worked and he’s the greatest kid now. But with my second, if I tried to do time out or discipline, the screaming would just go for hours if I’d let it. I really don’t know how to manage it