My son screamed too. A wind-up swing was a huge blessing for him. Car rides helped enormously too; I took him with me for every errand. I continued to breast-feed him, and not on a schedule either; sometimes the breast milk is digested very fast and the baby is hungry an hour and a half later. He was screaming for a legitimate reason. When we started introducing solid food that cut down on some of the screaming too.
I had to continue to exclude caffeine from my diet.
Careful not to get too vigorous with swinging and cuddling. Sometimes people think that if a little swinging is good more is better, and they chuck the baby around so strongly that the baby can risk Shaken Baby Syndrome.
It lasted all of six months with my niece. Absolutely nothing worked. We have a big family and took turns giving the parents a break.
I did hold his head so as to avoid SBS.
I had to do this (on doctor’s advice) for my own colicy daughter.
Good advice though!