nagging cough

I recently sent my horse out for some canter work for about a month, although I provided his feed and hay he was turned out in the pasture where there were round bales. About 2 weeks there he strated this cough...I took Cadbury to the vet just to be on the safe side and they said his lungs were clear and he was fine that maybe he got into some mold or something.....Well it's been 2 months now and he's still coughing and it seems to act up twards the end of our lessons like when he's tired...Could he have gotton into some bad hay at the trainers or could this be alergie related? This past weekend we were in a show for our FIRST TIME and he sneezed a BIG boogy on me!!!lolol Can horses come down with alergies? Cadbury was born here on my proporty and he just turned 5 at easter( hence the name Cadbury since he looked like piece o chocolate!.lolol..) and he has never had done this before..