The migraines you're having around your period, with one-sided pain and strong light sensitivity, are known as menstrual migraines. They're triggered by the sharp drop in estrogen just before and during your period, which is why the pattern repeats each cycle.
Next Steps
Keep a diary noting which day of your cycle each migraine starts, since that pattern helps confirm the link. Staying hydrated, as you're already doing, along with resting in a dark, quiet room during an attack, are both reasonable.
Health Tips
If these keep disrupting your month, please consult your gynaecologist about cycle-based options, who may also involve a neurologist for stronger relief.