Use anti diarrhea medication, for example Loperamide, it's available in every normal pharmacy (found it in France and Germany, no idea where you are). It will basically numb all your muscles in your gut and it will become impossible to poop.
For three days that should be fine, but you should reduce your food volume a bit.
This is unhealthy and stupid!!! But it works and is not crazy dangerous for your body.
P.S.:I guess you should just overcome your social fears and poop like a normal person.
I need to survive for 3 days without pooping, and eating as little as possible. I can pee, but not very often. It can't take up too much space. What food do I pack?
Please don't ask why I need this....