Poop labor!!

This is really embarrassing, but I hate pooping when I'm on my period. Mostly because my cramps are ridiculous to start with, but adding having to poop on top of that makes me cringe every time. To the point that I poop twice maybe when I'm on my period. Which also means that I don't eat as much to avoid this pain. Tylenol doesn't help..neither does any other pain reliever...i need help!! What do i do?! And does anyone else have this problem?