with the urgency of an emergency tampon

This is a phrase that indicates a very serious situation that is on a urgent timeline - it needs to be fixed NOW

As Ally jokingly posted a manipulated image of one of her friends appearing fatter than she was on the Gram, she recalled said friend had multiple embarrassing real images of her. So, with the urgency of an emergency tampon, she removed her post and then shared a flattering image of her friend, who was named Abby btw, and tagged it "Bad Bitch!"