Oh, Tiktok, I know you are the Mumsnet guru of all things breastfeeding, and so I say this with trepidation, but I think you are wrong!
My son had cmpi and was identical, exactly the same as the OP describes her daughter. Nobody believed me, either, for 5 long and hellish months. I really think trying to find some kind of mental health "cause" for this problem is not helpful. It would've pushed me over the edge, that's for certain.
Signs and symptoms of my son's cmpi:
Colicky symptoms 24 hrs a day with no daily pattern (ie definitely not 5 o'clock colic)
Gallons of sick (way more than normal posseting)
Lots of painful wind, painful enough to wake baby from a deep sleep with cries of pain
Inconsolable crying virtually all the time, even when coming up for air during feeds
Very frequent feeding - 1.5- 2 hourly
Always reluctant to stop feeding
Poo virtually liquid
All the above are classic signs of a dietary intolerance. It was very, very hard to cope with, but had nothing to do with anyone's mental health!
I am not sure why you say that there is nothing in the OP's posts that indicate a dietary intolerance? As far as I can tell she is experiencing pretty much exactly what I did 
I feel so terrible disagreeing with Tiktok......