Take her back to the dr. only they can tell if the cough is from Post nasal drip (due to allergies) or if it is in the broncular tube with an infection.
Honey- Get local honey from the farmers markets. 1 teaspoon a day can help her body get the immunities it needs to help with seasonal allergies.
Aslo, Honey before bed 1-2 spoonfulls will coat the throat. If it is post nasal drip it will help with the cough.
What is her diet like? Does she get home made soups with garlic and onion cooked in it? if not Try some that will help boost her immunity.
'How much milk is she getting? It could be helping the cough get worse not better. How much fresh fruit does she get? Does she eat yogurt? How much rest does she get? All this can help build her immunitys.
Also, my son had seasonal allergies. He had ezecema when he was a baby. We went Gluten Free in Nov for him and since then it seems to me his seasonal allergies have lessoned or disapeared.
We also have a hepi air purifier ($450.00) from an allergy store. We keep it in the kids room. It makes a huge difference. The cost, is worth it to us.
Before bed, we rinse him off. and change clothes to remove the pollen that has fallen on him from playing outside. That can also help with allergies.
As far as the antibiotics.. Missing two doses.. next time keep going until you have done the full time, but it should not make that much difference. I doubt that it is why she is coughing.
Good luck