Yes, the fever could be the cause. I would suggest not to worry - such hair loss is always temporary - usually will normalize in two or three months again.
Minoxidil can be used for other types of hair loss also including female pattern hair loss - but it is to be used with caution at such a young age. I would suggest - do not use it, hold it off, I am sure hair loss will return to normal in tow or three months again.
About the blue nails, I would suggest that you discuss with your doctor. It probably means nothing, but you should rule out that it is cyanosis - inadequate oxygenation of the blood. This can be due to heart defects like congenital heart defects, lung
causes like bronchispasm and blood causes like Methemoglobinemia.
But most likely it is not cyanosis at all - simply a bluish discoloration of the nails which is present in many people.
Take care - for the hair loss I would suggest a wait and watch approach with high protein high iron diet - as for the nails it probably does not mean anything at all bt discuss with your doctor about cyanosis.
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Dr. P.Jyoti, MD.