For active children who are in school, it can be normal to have several episodes of fever
a year associated with upper respiratory infections like the common cold.
However, several fevers a month is quite unusual and somewhat concerning. Have you measured her temperature and documented a fever, or does she just feel flushed and warm. It would be important to document the actual height of the fever as a first step.
The cough may or may not be related to the fever. The best first step is to think if there are other associated symptoms. For example, does she spit up blood when she coughs, has she lost weight in an unexplained way, does she complain of night sweats, does she have swollen glands, does she have any bone or joint pain, does she have any skin rash, has she had any recent foreign travel?
What might be going on with your daughter is difficult to say. There are numerous inflammatory and infectious possibilities, as well as the rarer possibility of a cancer. It is also possible that she just feels "flushed" and also has asthma
or some other benign cause of cough.
Nevertheless, preparing answers to the above questions and then going to see your pediatrician
as soon as possible is the best way to get to the bottom of this.