Thank you for your query and excuse me for the delay in responding.
As you mentioned that your daughter is daughter is having a running nose and cough
for five weeks which has not responded to various courses of antibiotics, she may be suffering from viral infection which shall take its due course. However the fever
and the rash
warrants a work-up. You should discuss with your doctor and, if required, get a blood test
done to know the exact situation. The viral infection may be the cause of the rash too. Depending on your location, the rash may be the initial rash of measles
I hope I have answered your query to your satisfaction.
Wishing your daughter an early recovery..