I could have written your post. My son is now 21 months and had a cough since he started nursery at 1yo. He has had many viruses and a couple of serious illnesses requiring trips to a&e but always had this bloody cough that wouldn't go away. (He also had a cow milk protein allergy and had prescription milk/stuff for his bath/cream etc but is pretty much fine now food wise but constant use of the bath emollient and creams for his eczema keep his skin lovely.)
Cough was always only at night after going to bed, sounded 'dry' but also sounded like there was phlegm there that just wouldn't come up. Sometimes he would cough so much he was sick. After just recently seeing a consultant (after months of questioning GP's about his cough) he now has 2 inhalers. I was told 'we're not calling this asthma'. After being ill, almost constantly all year, I was told his lungs are probably inflamed and his ribs are/were splayed out at the bottom which means that the diaphragm is working too hard.
He has to get the brown inhaler as soon as he wakes up and just before bed, it states 'preventer' on the box (don't ask me the proper names!) And he only gets the blue inhaler 'reliever', if he's been running around. The consultant said he is curious of the affect of the blue inhaler as he may not need that one.
I noticed a positive effect the first night, it was almost amazing and hand on heart, and I hope I don't jinx things here, he hasn't had a night time coughing fit since. Do you have any pets? We are farmers so DS has had contact with many animals but I remember the consultant saying he was pleased we didn't have cats as pets as they are the most allergenic animal you can have in your home, didn't give two hoots about the dog but did say it was good that the dog was in the house before the baby was born.
Stick with the inhalers, it's made a real difference for us and the change in our son is unbelievable, probably due to getting undisturbed sleep aswell. The consultant seems confidant that it will be something he will grow out of. I hope this helps, and hope things work out for you.