Thank you for your query on Healthcare Magic.
Some times paleness is due to low hemoglobin
which is know as Anemia.
Anemia may be the cause for her paleness, tiredness
, and for her increased heart rate
In anemic conditions, there will be some murmurs audible over the heart which are known as functional or innocent murmurs.
Investigations like complete blood picture to know the level of hemoglobin, 2D Echo to know the structural abnormality of the heart are required.
Therefore I advise you to consult the Pediatrician
for the investigations and treatment.
Hope I have answered your query.