Praise be to Allah.
We praise Allaah for guiding you to an understanding of the seriousness of backbiting and its evil, and for hastening to give it up. We ask Him to help you and make you steadfast in that.
It is well known that many women become depressed and anxious during their menses, especially at the beginning, and that a woman’s intellectual state is not normal during menses. Most women feel pain in their backs or lower abdomen, and for some of them the pain may be more than they can bear, so they use medicines and painkillers. See question no. 43028.
Undoubtedly what you are feeling is one of the effects of menstruation but all you have to do is be patient and seek reward, for nothing befalls a Muslim, not even anxiety and grief, but Allaah will expiate some of his sins thereby.
You should keep yourself busy with work, study etc that will benefit you, for free time makes worries worse.
There is nothing wrong with a menstruating woman reading Qur’aan without touching the Mus-haf, and that will distract her and make it easier for her.
And Allaah knows best.