Thank you for your query.
I suggest that you consult your doctor for the problems being described by you. Without examing the lesion that you are describing it is difficult to tell you the reason for them. I can only think about some blood borne infection settling down in the fine capillaries of the fingers where the blood flow becomes very slow. This can follow some throat infection
I hope I have answered your query to your satisfaction.
Wishing your daughter all the best.