Shusshing and gently bouncing up and down was the only thing that worked for me as a dad but the only problem was after 30 minutes my arms got sore and my mouth was dry. The screaming would start again.

Don't worry there is hope it was just around three months and things are much better now. My daughter is four months. Not sure how long it will take for your son but even though it feels like forever and ever and ever it will change.