Cup in your handbag

I have an irregular period and usually keep my emergency tampons, pads, pantiliners in a plastic makeup case to stash in my purse.I know I can't store my DivaCup in my plastic case so is there anything wrong with just keeping it in the cloth pouch it comes in and keeping it in my purse? Should I get a more sturdy case for it (I'm thinking about getting a cloth pyramid/tetra pouch from Etsy).

Thanks!