Dear Pete
It's not unusal for dry coughs to last a long time - my mother had one that lasted 3 months! - I've had a similar cough which has exacerbated my condo. I too went to my doctor but didn't get any antibiotics - in fact the doctor should have taken a sputum sample to test (bronchitus is just a guess otherwise); I used to suffer from bron, and it's not uncommon for it to last months, if indeed that is what it is.
Don't know what to suggest on the doc front but a home remedy is to put a large bowl of boiling water beside the bed when you sleep, add menthol ("vicks") and let the airways breathe that in as you sleep. There's also a special herb tea I used to try which really helpd (agggh can't remember the name but if you want to send me a private mail I'll check it out for you). You don't say if the cough is worse at night (mine usually is) but I wouldn't go worrying about it being anything very serious just yet... Best of luck and let us all know how you get on.
B.