Hi
With Emirates after you have the medicals in the UK they tell you in your instructions not to take any Cough medicines or cold and flu remedies for 2 weeks before you fly to Dubai as they can show up a positive result in any drugs screening they may give you.
I am sure that Your airline are aware that these medicines can cause a positive response, so don't worry too much, or speculate about what they are going to do. I'm sure that this is not the first time they have had to deal with this. As long as you know you are clean it will come accross to them that it is an unfortunate mistake.