I have the same problem which I, too, thought might be caused by Omeprazole. I did find, like CalGal, a link between Omeprazole and
it was also causing itchy skin down my spine area. Changing my PPI to Lansoprazole recently has not made the slightest difference, and I continue to cough all day and all night, a dry, irritating cough.
I also have gastritis, oesophagitis, a Hiatus hernia, none of which had been symptomatic other than nausea, and a lack of desire to eat.