K so is the heat source a heat lamp ? And is it over the center of the tub or one side? Can you post a picture of the full set up? I think it’s important to know what the temp is in there- need thermometer - how is duckling doing today?
The open mouth breathing could be panting, if it’s too warm in the brooder.
This is why it’s important to find out what the temperature is first before trying to find an antibiotic that she can have and what the dosage is for a respiratory infection if that’s what it is