Walk down the Scary Aisle at the grocery store some time, for tampons did not have universal adoption, and what women were using right before the invention of the tampon is still vibrantly in use today (with some notable upgrades), the noble disposable sanitary pad (or napkin for the Brits).
I am going to direct you to my favorite outsider-history website, the Museum of Menstruation, which is one man's private historical passion writ large on the internet. Set aside some time, because you will fall into the menstrual history hole. But what is cool, for the time right before the tampon, is that there was a survey done by Johnson and Johnson of college women which tells us exactly what they used. So we know, in excruciating detail, just how American women of means, independence, and education physically managed their period right before tampons came on the market. Which is neat!
- Pads of this period were square cellulose, came up too high in the front for women's taste (or need), and women usually cut them into a rounder shape to be more comfortable. They also sometimes powdered the pads, put commercial underarm deodorant on them, or put petroleum jelly on them to reduce chafing. Reusable cloth pads were not part of the survey, but perhaps college women didn't like them as much, with their active flapper lifestyles.
- Sticky-back pads had not been invented, and so they used belts to hold them to the body (these were like small garter belts, there's pictures on the website), and they mostly pinned their pads to the belts with safety pins. Pad belts were still in use through the 1970s, if you have a 60+ year old woman in your life you are comfortable with, ask her about belts for a fun impromptu oral history!
- Rubber underpants of some sort were commonly used (like cloth diapering), there were also these rubber butt-apron things, but nobody in this demographic much liked these.
- Contrary to our contemporary false ideas of Ye Old Period Tyme sponsored by Tampax, the college-aged women did not sit home the entire time before tampons were invented wishing they could rollerskate and skydive, but they did feel the annoyance that they had to change their fashion choices, as the big pad + belt + rubber pants did not work well with the hot 20s fashions, and the surveyees mostly complained about the size and shape of pads. But evidently they made the pads work and got on with life for those annoying 3-7 days.
So now you know how to be a flapper and have your period in 1920s America!