My DD was still on omeprazole at 3, when she suddenly decided she'd had enough medicine for a while and preferred to vomit instead. Thankfully at almost 5, episodes are now few and far between, but absolute bollocks to reflux stopping when they can sit upright - they're just less likely to choke on it, is my experience (with both DC).
We saw Keith Lindley at Great Ormond Street, who had been recommended on MN several times before we were referred. DD had a 24hr probe test which proved severe reflux (which we kind of knew anyway - average 200-250 vomits per day) but crucially, also proved that it wasn't overly acidic, which was a very pleasant surprise for everyone. DD has a reflux-related cough, worse at night, and associated allergies, but is on an antihistamine for that. Mr Lindley told us that if the reflux was acidic, it could be causing cell changes in the oesophagus. If not acidic, then the cough was annoying but not serious, and the reflux was more about interfering with quality of life than serious long-term health effects. (Pretty sure I've remembered correctly, it was a while ago now).
After the 24hr probe, we chose simply to manage the symptoms and not find out the cause, which was the next step via endoscopy. Obviously had the probe shown that damage was being done, we'd have had to do the endoscopy.
I'm fairly sure Mr Lindley also said something about a 95% rule - something like 95% of babies grow out of reflux by 6 months, of the remainder, 95% by 12 months, of the remainder, 95% by 18m, then 95% by 3 years, then 5 years, then you're left with longer-term management of a few.
In our experience that was fairly true - DC1 did improve significantly around her 3rd birthday, DC2 was horrendous at 16m, much improved at 18m so we stopped the omeprazole, etc, and totally reflux-free at just turned 2.
For allergies I'd recommend Dr Adam Fox at St Thomas's/Evelina - maybe a fun midweek trip to London is on the cards
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Good luck, but honestly, it will get better. DS was dairy-free and medicated up to the eyeballs at 16m, fine just a couple of months later and our lives were transformed overnight. Amazing how quickly you take for granted not having to cart around 3 or 4 spare changes of clothes, a bundle of muslins and several packs of wipes!