do you mean diarrhea instead of constipation?
If you mean diarrhea, I have a story for you. A public story.
I was in the entry/reception area of a very large upscale retirement living facility making a delivery when I had a sudden urge to use the bathroom. I asked the receptionist where it was and she directed me down a hallway.
As I am calmly walking down the corridor, everything comes loose. And I mean in the most horrifying way imaginable. Every step created an ooze. My cheeks cannot clench hard enough to stop it. My colon literally emptied completely. By the time I get into the stall, even my shoes are destroyed.
I am now stuck in a public but private bathroom and everything on me and my lower body is covered in feces. My cell phone is right OUTSIDE the facility in my car. I am stuck. I could have stayed there for hours with no one using this bathroom.
The only good thing is that my shirt covered my tushie, just barely.
After cleaning up the best I could, I suck it up and walk calmly out the door. I have no doubt I smelled and I had brown streaks on my legs.
I was very embarrassed. At least ten people are in the lobby as I walk passed them. I felt sorry for the janitor that had to clean up what I was unable to do under the circumstances.
What would you have thought of me as I walked out? Would you have had compassion or laugh or what?
I like to think after the initial shock, I would have had compassion.
I have MS and that is the sorry truth of the matter. Lousy things happen. This little event happened over a year ago. I think the only one that remembers it at all is me and unless prompted, I forget about it.
I like to think it makes me very unpredictable.
It is not easy and you have my sympathy and empathy. And your incident happened at home!!! How great is that!

If it happens in public, well you know in advance, you are not alone.