Sparkly, trust your instincts, go to A+E if you feel this cannot wait til tomorrow. If you don't go then make sure you go to the doctors tomorrow.
Chances are, its just a viral infection and it will clear itself, but he might have developed a secondary bacterial infection which will need treatment. You are perfectly entitled to raise your concerns if he has trouble sleeping.
FWIW, this has been a house of coughs on and off since xmas. We have all had it and it lasts for AGES and AGES. I have been to the doctors twice with mine and sent away to be told its viral, nothing we can do - fair enough, but its worth checking.
Our coughs are all caused by sinus congestion so anything to reduce congestion will be effective, medised if he is over two, but dont mix this with a cough mixture. Put some Karvol on a tissue near his bed and prop it up on a couple of big books. Agree with the dusty teddy thing too. Change all of his bedclothes and dry them indoors (just in case its a pollen reaction). You can also go and sit in the bathroom with him and boil a kettle so he can inhale the vapour.
Im sure he will be fine, there is a lot of this going around just now - but if you are worried, get him checked, there is no such thing as a over anxious parent. IMO i would avoid out of hours and see your doctor, tell him you are worried.