Should I go my manager about my coworker's IBS?
How do you know about their IBS?
I went to their workplace, I saw they have a sign taped to their monitor
You shouldn't talk to your manager about your coworker's health issues. That is a private thing and your coworker should be the one who is telling people if they feel like it.
She is embarrassing other individuals in the place and I am doing it for the good of all.
When someone has a health issue others usually keep that private. It is not your business to talk about.