I carry my handbag at all times. Its utility in transporting maxi pads is of minimal relevance; probably 90% of the time I have no "menstrual gear" in the handbag. I have money/cards, makeup, a little notebook, my cell phone, very often a book I'm reading and/or my day planner, and approximately forty pens and highlighters in various colors. And cough drops, and keys, and gum, and whatever little items I may have purchased during the day (or the previous day but I forgot to take them out), and a tiny light used for reading books in the dark, and some recent mail, and my iPod, and mystical healing crystals, and god knows what else.
So obviously, since you're getting different responses here, the choice is up to you as to whether your character carries hers. Remember, though, she may have a pseudo-handbag: students carry backpacks or some other bag, so women students may just throw all the normal purse items into that; mothers lug around diaper bags, and sometimes all their purse stuff goes into the pockets of it. Also, some women--those who are on the go a lot, driving different places several times a day--may use their cars as purses. I mean, all their stuff--lipstick, hairbrushes, a couple of books she's currently reading, cell phone, day planner, etc. etc.--may just be tossed in the car.
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