What could cause difficulty swallowing, pain on swallowing through to back, distended painful stomach, constant cough. No diarrhoea or constipation?

Esophageal. Your symptoms are probably due to an esophageal motility disorder; other causes are possible stricture(scarring) large hiatal hernia or an obstructive growth, and would best be evaluated by a gastroenterologist if they persist.
Trouble swallowing. It's impossible to say in this format you need to be evaluated as soon as possible . This could be a serious condition. You don't say how long you've had it , when it started or how it started and what you've done about it. Good luck.