Menstruation has a good relation to sore throat and fever, according to ayurveda, due to rakta strav - flow of blood or blood shedding, always vata dosha is aggravated. Aggravated vata leads to excessive thoughts, emotions and actions. In this way disturbs Jatharagni - digestion, which produces a lot of kapha - ama in menstrual periods. lately, this ama carried away by open srotas - channels - is responsible for fever, headaches, weakness, sore throat, nausea, dysmenorrhea etc.
I would say you to properly inspect your daily routine and lifestyle during the week before menstruation. suggestions are that you should have laghu supachya ahara - very light and semi-liquid foods, in that week. try to gargle regularly on those days and avoid junk, unctuous foods.
also ask your mother or maternal or paternal aunts about this, if they have also gone through the same. If so, ask them about the solutions they adapted. mostly it would work on your body.
Next Steps
consulattion if you feel necessary
Health Tips
healthy lifestyle, daily light exercise, breathing exercise