My baby wont stop crying

Hi my baby is 4 and a half months old and since birth has done nothing but cry. We have seen the gp so many times, we havr seen a pediatrician and they said she has silent reflux and a possible cows milk intolerance so she is on omeprazole and special formula but none of which has seem to make a difference. She has never slept for more than 4 hours at a time. We sleep downstairs as I have a 4 yr old also that the baby wakes at night if we are upstairs and my partner can not also sleep with the baby in the same room. Me and my partner haven't shared a bed since a week before baby was born. We seem to argue all of the time and babies crying is driving us all crazy. 
I feel like such a failure as I can't seem to do anything to settle the baby. Im so grouchy all of the time and often snap at my 4 yr old. Im losing my mind! 😳