It's a perfectly normal phase that some babies go through. Numerous studies have shown that 'colicky' babies do not have any more wind in their systems than placid babies. Screaming starts at 3-4 weeks and peaks at 6 weeks. Often called 'purple crying'. Most babies that are shaken to death are killed during this phase apparently.
DS1 was like this - my lovely HV gave me a copy of 'The Happiest Baby on the Block', by Dr Harvey Karp. I cannot recommend it enough!
In short - follow the 5 Ss:
1.SWADDLE - use the arm lock method, keeing the swaddle resonably loose over the chest. A Miracle Blanket is designed for just this. Otherwise google - there is a clip somewhere of a dad arm locking with 2 receiving blankets. Your baby will obviously resist the swaddle - keep at it with steps 2-5...........
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SIDE/STOMACH - crying babies freak out when on their back (it activiates the startle reflex). Swaddle, cradle your baby on his side then.......
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SWING - dance from side to side really, really fast, making sure your baby's head is snug in your arm. This makes the tiny, imperceptable shoogling he got in the womb. Or use a baby swing on the fastest setting.
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SHOOSH! SHOOSH! - say this into your baby's ear - really loudly. It must be louder than your baby's cry for him to hear. You'll feel damn uncomfortable doing this, but a baby's cry is louder than a hoover. This white noise is supposed to mimic the sound of blood rushing in the womb. Hairdryers, hoovers, washing machines are also good sources of white noise, but they never worked for DS1.
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SUCK - breast feed when he's calmed down, or use a soother.
These crying fits will come in a cycle of 3-4 every 15 mins. Thus the first few times, it will take you a good 15 mins to calm him. When the first crying phase eases, you can ease off the shooshing, shoogling, but do expect it to start up again.
I was suicidal with DS1 until I started the 5 Ss. Within 24 hours of practising the 5Ss, I was able to calm him almost instantly. Some days he would be bad, but it never took me long to calm him.
Good luck
P.S. Before you start on all this - be confident that he doesn't have reflux (vomiting badly after feeds etc). As a matter of course, prop up the mattress in his cot anyway.