DS (also 6) had this last week - started v bad headache Mon night - high temps/headache/soreness/sickness on Tue - took to drs Tue pm and was prescribed penicillin - one dose big difference, two doses he was back to old self with a slightly sore throat.
Hope your DD feeling better soon - we were told to continue with Calpol & Ibuprofen whilst giving the penicillin.
Sounds like frozen lollipops good way to go - helps numb the throat while getting liquids down her - maybe ice cream?