I went through similar with DS (now 12 months). I had to go to a few doctors before I found a paedetrician that would believe me that he had CMPI and reflux. He was put on omeprazole, nutramigen puramino, and carobel (you don't need a prescription for carobel btw, it's in most pharmacies).
Also a lactation consultant diagnosed posterior tongue tie and we had that fixed at 6 weeks.
All of this improved him but bit-by-bit. Constipation is a side effect of a few of these things but our paedetrician recommended a little extra water in his bottles, and I also put him on baby probiotics and that soon went away.
By 12 weeks he was sleeping 9 hours straight and by 16 weeks he was mostly a happy baby. Introduced solids at 17 weeks and suddenly he went from 15 min daytime naps to 90 min naps. Also lots of tummy time as being on the tummy closes the valve to the tummy whereas being on their back opens it.
The medication (and prescription formula if necessary) is key though, so don't be afraid to get a second opinion. Or, like me, a fourth opinion. He is still on his meds but I will try weaning him off them soon. You'd never know he had reflux since 4 months and everything clicked into place but it has come back when we reduced the medication in the past.
I really feel for you but it will improve! Good luck.