Ok so just got Allie's results back. It is bacterial (yay) so the vet says that she doesn't want to give any steroids now because that can interfere with the immune system fighting off the infection (as steroids suppress immune function).
So Allie is to finish the antibiotic course she's already on, then I've got to do a few test rides to see if there's any more coughing. If there's not, fantastic. If there is, then I've got to take her back for another trachea wash and start anti inflammation treatment.
Hopefully it's just a bacterial infection that she's picked up from the stupid racehorses.