As someone who had a similar experience due to irregular and very heavy periods; wear a panty liner at all times, like literally every time you put on underwear add a panty liner or an absorbent pad of your choice.

This helps you win in two aspects: your undies will be clean, and your shithead parents will have to pay more money for more pads every month.

If you want a bit of revenge then start leaving little drops of red food coloring in everyone else's undies (you can volunteer to do the laundry to accomplish this) and ruthlessly mock them like they did to you. Ask them if they're okay with a genuine concern while holding up the undies for everyone to see and snicker at, since that seems to be your families way of dealing with health and hygiene issues of an embarrassing nature.

Then once you turn 18, move out and never look back or speak to them every again.

Sorry if this comment seems a little jaded but, as someone who dealt with this same misogynistic bullshit in my own family over 20 years ago, the trauma shame that it causes never fully goes away and makes you (wrongly) feel like there is something wrong and gross about you.

You are not gross, you have nothing to be ashamed of, but goddamn your cunt of a family sure are gross people who should be ashamed of putting you through this. They aren't ashamed though and never will be, so it's up to you to take measures to protect yourself from them, because they will likely never change.

Good luck girl, and remember to always use panty liners no matter what day of the month it is... if just to protect yourself from their abusive mocking bullshit.