PMR Cough?

This is a long shot, but you could try asking for a decongestant.  I had a similar problem some years ago which was eventually solved in this way and while I am still rather hoarse at times, I know that is caused by acid reflux.

I haven't been bothered by the cough since then.

Sorry - what did the GP overrule? I do find it arrogant of a GP to dispute a specialist's advice or attempt to control a situation. Are the inhalers an attempt to control the cough or has the cough arrived since using the inhalers? 

Did it occur to the specialist to test for non-acid reflux? Is it available in the UK? It is new and probably only available in specialist centres.  Acid and non-acid reflux are different things and the medication used for acid reflux won't alter the non-acid problem. A technique called "multichannel intraluminal impedance monitoring combined with pH monitoring" can be used but how available it is I'm not sure. This is extracted from a 2011 paper:

"A significant number of patients with typical reflux-indicating symptoms do not respond to PPI treatment; nonacid reflux disease may be underlying in these patients. Nonacid reflux is common and causes symptoms very similar to the classical symptoms of GERD. Combined impedance-pH monitoring helps us to diagnose nonacid reflux disease, and patients with insufficient response to high-dose PPI should undergo impedance-pH monitoring where available. In contrast to pH monitoring alone, the combination of pH monitoring with multichannel impedance testing is a powerful tool to detect acid and nonacid reflux when performed while the patient continues to take a PPI twice daily.

Current treatment approaches are limited; however, promising clinical trials are underway. The contemporary approach includes intensifying the same lifestyle modifications recommended for GERD. Baclofen (10 mg four times per day) before meals may be tried as suggested by small clinical trials. If both approaches fail and the patient requires a more definite therapy, a surgical approach may be considered. A requirement for surgery is that nonacid reflux be diagnosed with an impedance study because, until previously, failure of PPI treatment was considered to be a negative predictor of symptom improvement following antireflux surgery. It is presently unclear to what extent drug development will add further options in the near future – the clinical trial activity, however, appears promising."

Was it Baclofen the specialist recommended? On what grounds did the GP say no? The medical literature mentions that about a third of patients do not respond to PPIs - possibly your PPI is simply not working and it is acid reflux after all. Have you tried ranitidine (Zantac) or another non-PPI instead? I understand that fundoplication surgery is a final resort in non-acid reflux. Using google, look for "what is nonacid reflux disease Martin Storr" to get the paper I took that extract from - had you seen that before? 

Also using google I think you may find life-style change advice that might help if you haven't already tried it - I imagine that includes small meals, identifying trigger foods and so on, raising the head of the bed. I know there are also some experts who believe that reducing carbohydrate intake drastically can also have a dramatic effect on reflux and a small study was done which demonstrated that. 

And frankly - if your GP is that unhelpful I would seriously consider finding another. You need one who will work with you and your specialist who is doing his best I imagine - not one who is plain obstructive.

On a final note: I have just been googling and found a forum for Barret's oesophagus patients talking about a similar problem to yours. Some doctors claimed that swapping from omeprazole to lansoprazole would help - whether it did or not wasn't clear. However one contributor said:

"I, too had a cough. And sometimes bad bile reflux. 

Bile reflux in itself can cause a cough! 

However I have now cured both the cough and the bile reflux, and am still taking Omeprazole! 

It is certain, from my experiments that Omeprazole is the cause of both. Excess Omeprazole is metabolised in the liver, so it's hardly a surprise that bile production is affected! 

The cure for both is to minimise the dose: little and often. I have been taking 1/2 of a 10mG capsule every 8 hours: first thing in the morning, about 3 p.m and again before bed."

Worth a whirl maybe? Do tell me how you get on - your question has led me to info I'd not come across before and which may well be useful in the PMR story. GPs seem totally in love with PPIs - I had never seen before that they don't work in a third of patients, and they do have some unpleasant side effects which I did know as well as causing osteoporosis. I wouldn't take them if you paid me - the local hospital tried to put me on them a couple of years ago and then I discovered they were not covered by the state health system here, I would have to PAY full cost to take them. I'd never taken them before and decided I wasn't taking them now! They didn't appear to make much difference! If I needed anything I'd get some ranitidine (Zantac).

This may not be relevant, but I have a CPAP machine, my last cold I turned the humidity up high and slept wonderfully. No coughing at nite. Have you tried a humidifer, more than what's on your furnace? ( I'm making some assumptions)

I also have a problem with reflux

I have been taking nexium 40 for a while

when I started on the prednisone the reflux was really troublesome, so I take nexium 20 morning and night every day and the reflux is under control.

The systems of my reflux is a cough, no other pain, so maybe it could be part of your problem

Are you on  medicine for blood pressure/heart? One that is often forgotten is ACE inhibitors like ramipril (anything ending in ....pril ) they are notorious for causing cough.

just a thought you are not on blood pressure medication? as this gave me a cough, and a few other people I know.