Can Colleges See Why You Choose to Withdraw from a University?

I went to a college where I got in trouble for something stupid. They give me an option to withdraw or be expelled. Of course, I choose the withdrawal.

Now applying to other universities, there is a column where it asks if I have ever had to withdraw from a university before disciplinary actions. The answer, is again, yes. But my question is do the schools that I’m applying too already have information about the situation?

And if so, how do I explain this situation, where it is not only humiliating but might stop my admission to the School because of how crazy I acted.

Grades, extra curriculum activities, and the other aspects of my applications are strong.