Hi! First off I just wanted to say I hope that you are ok, i know only too well how horrendous this experience is! I wrote nearly the same post just over a month ago whilst awake at 5am crying my heart out with my little boy screaming!
He screamed from day 3...continuously...all day and night, would not be put down, tilting cot, infacol etc all did not work, finally I took him to A & E in despair after he screamed for a solid 24 hours and choked badly on his feed!
He was diagnosed with cows milk allergy, we started a new formula (nutramigen) and carobel to thicken the feed to help keep it down, much like you, this only lead to more screaming and 6 days of constipation! His feed was then changed again to Neocate as this contains zero milk protein and he was given lansoprazole to ease the pain of the acid reflux and his thickener changed to a lesser known one called thixo D ..... it was a miracle....not overnight, it did take the full two weeks but I can honestly say I have a changed baby, he is so smiley and sleeps all night at 10 weeks!
What I am saying is that it feels like it will never end, you despair when they tell you to wait 2/4 weeks but it honestly all changes once they get the right combination, do not be fobbed off, gaviscon causes horrendous constipation, I would ask for a change and for an anti reflux medication alongside.
Sorry for the long post I just wanted to let you know I have been in your shoes.