Brief Answer:
Migraine headache can be triggered by menstruation.

Detailed Answer:
Hello! My name is Olsi Taka, I am a doctor specialized in neurology and I will try to answer your question.

Menstruation is a period associated with hormonal level changes and as such imbalances can manifest symptoms not observed during other days of the month. However there is no evidence of any pain related to the brain during menstruation. Actually the brain itself doesn't feel pain, it doesn't have pain receptors, when you have a headache it is related to structures like layers, vessels, peripheral nerves etc. So if read literally the answer to your question is no, the right side of your brain does not hurt when menstruating.

However if you mean headache involving one side of your head it might be in the setting of migraine. That is even more probable if also nausea and vomiting, increased sensitivity to light and noise, with pulsating headache.
Migraine can be triggered by many different factors (foods, lack of sleep etc). Among these migraine triggering factors in some patients there can be also menstruation (due to hormonal changes). There are forms of migraine which happen exclusively during menstruation. So if by your question you meant such headache, yes, it can be related to migraine.

I hope to have been of help.

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