Sounds like your child has very mild infection. If you don't worry about infection which primarily causes fever, then no major things to worry. Her cough usually will go away by itself, in a week or so.
If the doctor prescribed it over telephone and it is not anti-bacterium or virus, the need to take it sounds small. A soothing medicine may or may not work.
If you wants to use it, I guess it is ok to use it but just reduce the dose a bit.
You can try other ways like soup of pear and ice-sugar, etc.
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