Hello and thank you for posting your medical question on E health Forum.
From the history provided it seems that your daughter has post infectious bronchitis.
Usually once a infection subsides the residual inflammation of the airway causes persistent cough, this is called post infectious bronchitis.
The main symptoms here are dry, cough in paroxysms which persist in 8 - 10 % kids for a week to two weeks following viral respiratory tract infections but in some instances the cough persists for 4 weeks.
Productive Cough serves a purpose -- to clear out mucous -- and during the day, there's usually no reason to suppress it.
It is important to know that Antibiotics do not work for this condition, nor do cough medications in kids under 6 years age.
Here are some tips to help your child's cough and cold symptoms:
1. Lots of fluids to thin out the mucus that builds up during the cold virus infection so that it is easier to clear out. Try chicken soup, tea, broth, or clear liquids.
2. A cool mist humidifier - It can help with the discomfort of a scratchy throat, but make sure to clean it frequently.
3. Steam: Turn on the hot water in the bathroom and let the child breathe the warm steam for 10 minutes to help relieve congestion. Just be careful of little hands near hot water.
4. Saline nasal wash: A salt water wash to clean out the nose is particularly helpful in infants, who can't blow their noses. Drops are placed in each nostril and a suction bulb pulls mucus out of the nose. Be sure to sterilize between uses. Saline nasal spray may also relieve stuffiness for older children.
5. Honey can help Kids older than 1 year to prevent cough. It helps children sleep without coughing all night.
6. Get your kid to wash their hands frequently, encourage them to cough into their sleeve or elbow, and make sure they get plenty of rest.
You might consider to consult your kids pediatrician for an examination if the symptoms worsen.
I hope this helps.