My DS (9mo) was exactly as you describe!
Very agitated during feeds, endless trapped wind, lots of swallowing down of 'something' that made him grimace and shudder. His weight gain was very erratic, some weeks he would gain a few ounces, the following week he would lose...
After endless trips to the GP he was referred to a pediatrician who, at 4mo, diagnosed 'silent reflux' (i.e. no puking!) and prescribed gaviscon, ranitidine and domperidone.
At first the meds made a huge difference and his feeding went from 17-20oz per day to 30-40! However, his sleep remained terrible, he had constant cold symptoms, excema and fairly explosive nappies...cue further visits to gp and pediatrician who upped the dose of his medication as much as possible given his still very slight weight gain.
To cut a veeeery long story short (this went on for a further THREE MONTHS!!) our HV referred to dietician who diagnosed cows milk protein and soya intolerance. This was causing the snottiness, trapped wind and discomfort (not tomention the other symptoms you describe...)
At seven months he was put onto a hypoallergenic formula and almost overnight he was a different boy! His eating improved (milk and solids), his excema disappeared, his trapped wind vanished, and, with a little bit of very gentle sleep training (sssh/pat) he now naps and sleeps amazingly well!
Keep going back to your gp if you're not happy. Speak to your HV. Download the NICE guidelines for treatment of allergies in children. There's a section in there outlining how reflux should be treated, and stating that if symptoms persist despite medication, allergy/intolerance should be investigated. There is also a list of symptoms which are suggestive of an intolerance - very useful - our DS ticked several boxes!
Unfortunately, we stumbled upon this info too late. However, it is worth passing on as, sadly, many people's experience (on here and in RL) seem to suggest that a good proportion of GPs are ill-informed when it comes to reflux and allergies.
Be a 'neurotic mum'. Keep pestering until you and your little one are happy. Don't be fobbed off like we were.
Good luck!