Thank you for your query.
I can understand your concern. You mention that your daughter complains of feeling sick. What actually does she feel? Does she have fever
or any other specific complaint?
Sweaty plams can be due to fever or some nervousness
which she is not able to express to you.
You attribute the itchy feeling to dry skin
due to winter. Have you applied any hydrating cream and/or oil and observed if the itchiness disappears? In case it persists then it shall be advisable to consult your doctor or a dermatologist
I hope I have answered your query to your satisfaction.
Wishing your daughter an early recovery.