Hi my 21 month old DS has silent reflux. it is very possible in older babies/toddlers ad even children although most grow out of it before 12 months.
DS symptoms were abit like your little ones. Mainly screaming, bad choking (he even stopped breathing at a month old and was rushed to hospital) violent hiccups, arching, not sleeping a wink at night and we could also hear the refluxing going on in his tummy. He did vomit alot but it was mainly the irritability and choking, he swallowed most of it back again.
It was horrible the first 8/9 months and only got better when he got mobile and able to entertain himself but it was still hard as he was miserable.
We first noticed a big improvement at about 18-19 months and he still has it but it is more like indegestion now. He had alot of trouble going onto solids and was on stage 1 purrees till 13 months. Took till 16-17 months to be on normal foods. This is very common for reflux.
DS's paed said that reflux often gets worse at weaning (DS did) and again when they start crawling (DS did again).
Meds wise the hospital diagnosed GORD at 4 weeks after the choking episode and gave him gaviscon. That didn't work so they gave him LOSEC and Domperidone. This helped about 50% with the irritability although he refluxed/choked just the same. There was no cure for him other than waiting and it was awful. he was my DC 5 and I had no idea what sleep deprivation was until I had him (and I had had twins before him!!). I think walking helps (DS was 14 months) aswell as eating solid food.
I breastfed for 11 months and cut out dairy/soya for 2 months with no difference. i also tried the colief incase of lactose inolerence.
Don't feel bad about sleeping him in a car seat, DS 'slept' (well we tried anyway!!) in a bouncer many nights. often me and DH took it in turns to hold him. Movement helps so we got him a hammock and that helped, he slept 5 hours a night in that (from 20 mins), music helped too, he had a little gloworm and lightshow.
I would go for the observation. The hosp saw DS having his reflux episodes which helped convince them. I also wondered if you had an Coeliac disease in the family, just with you mentioning it may have got worse with weaning as that can happen too. They will prob test for that in hopsital.
Anyway good luck and hope it gets better soon.