I don't know where to begin 
My LO is 9 months old. He suffered with constipation early on, from about a week old. We tried various formulas. He was an unhappy baby from this age onwards really. The doctors said it was colic and that "babies cry" but this wasn't a normal amount and he was hysterical. The HV said it was reflux. They initially said CMPA so we went down the allergy route and tried a hypoallergenic formula but it was awful. We finally settled on kendamil formula, he has a small amount of omaperazole for the reflux and we add carobel to his feeds.
He has never slept through the night. He has, in earlier times (age 3 or 4 months ish) done 5 hours then awake a while then another 5. But this was always sporadic and would last a couple of nights then back to stirring constantly. Its now been about 4 or 5 weeks of virtually no sleep at night. Even before this, we would be lucky if he had an hour in his cot before stirring. He wants his dummy, or just wakes in general and cries even with his dummy. He never just goes to sleep for a block of a few hours, ever.
We managed to get a fairly decent schedule on the go when he was 7 months old (he didn't sleep through the night, this is just to show nap times):
5.30 - wake
7 15am - nap
8.30am - wake
12pm - nap
2pm - wake
5.45pm - start bath and bed
6.15pm - down in cot
He initially settled in his cot for an hour then wed put his dummy in, rub his back etc. Then again an hour later then he'd wake every 20 mins until I'd cave and put him in our bed at 11 or 12 out of exhaustion. He will now not settle in his cot at all. He screams endlessly and we've tried various sleep training methods over the last 3 months. He will literally keep going all night. We give up after 4 hours of him crying non stop as working full time it isn't feasible. He now doesn't even settle in our bed. My other half has been up in the living room with him the last few nights midnight until 4am. It's relentless.
I've been convinced since he was a couple of weeks old that there has to be issues with his tummy/bowels. He wriggles and can spend a long time trying to get one trump out. We have been referred to a pediatrician but I've seen one before and they basically said he's fine and will grow out of it. We're at our wits end, we can't function like this. At 9 months we should have our evenings back, baby should be happier after a decent rest but he's often cranky and cries all day as he's over tired. We've bounced from illness to teething to a cold and I wonder if its just constantly something like this unsettling him?! Or if it sounds like there is something wrong with his tummy? Or we just have a bad sleeper and that's that?! We know a lot of people with babies the same age and no-one else is experiencing this extreme sleep deprivation at this stage. My life consists of work all day and trying to get him to sleep all night. I'm lucky if I get 3 hours and its breaking me.
Any advice or wisdom would be much appreciated! X