could you get an infection while swimming specifically because of your period?

So I know you can get an infection anytime. But my mom tells me that when I'm on my period everything is open because the blood is leaving and stuff and so I'm more vulnerable to get an infection. She's never let me swim on my period, ever, maybe only if it's my last day, and she won't let me wear tampons or cups either, so that I don't break my hymen or whatever.

Thanks for your answers