G'Morning S., Your Dr. didn't say when she would be able to return to school? That's strange. I have had walking Pneumonia several times in my life time. Grrrrrr being an adult and sahm mom I didn't worry about it much, but I stayed home at least a week. Until my chest stopped hurting and the coughing was controlled.
You didn't say how old your daughter was, but I would call the Dr. back and ask questions. Schools do not want children back, who haven't been temp free for 24 hours.
Coughing into your arm sometimes doesn't work well with children, they try but don't always make it soon enough.
So my advice keep her home until she feels alot better, it wears you out. Call your Dr.
God Bless, praying she is better very soon
K. Nana of 5