Hello from JustAnswer.
The most common cause of vaginal itching, either during your period or otherwise, is a yeast infection of the vagina. There are other infections that can also cause itching, such as bacterial overgrowth of the vagina, but they less commonly cause itching.
There is no ready way to prove whether there is a vaginal infection at home, although some women may chose to use an over the counter antifungal medicine to see if the symptoms improve.
If I can provide any further information, please let me know.
I thought you said that you were having vaginal itching but no other symptoms.
However, it would be fine to use any over the counter pain medicine to help ease any pain that is present.
Itching is different than pain. Soaking in warm bath water can help to ease the itching. It also would be OK to take an over the counter medicine for itching that contains an antihistamine.
Then the next step would be to try the above medicine.