Will something I got expelled for in high school show up when I apply to a university?

In high school, a friend and I one time decided to skip (as in those days we quite often did) and paid homeless people to pretend to be our parents. Well, the secretary who answers the phone happens to know my dad (1 in 3 chance it would be the one that knew my dad) and calls up my real dad to tell him I am skipping. The next day we are making prank phone calls at my house and she decides to call our school. Though I should have probaly not allowed this to happen, she ends up giving a death threat to the secretary. Next day police come in and threaten to take me in if I don't reveal that it was her, which of course I do. She and I both are expelled (though I didn't make the call or even speak on it, because it came from my house I was punished).

Well, on the university application, here is what I have wrote. Keep in mind I haven't submitted this and I am wondering to be completely frank if I don't even mention this if they will find out. I don't want to jeoperdize my chances of getting in by not mentioning this. Any input would be nice!

"When I was 16 and in high school, a friend and I foolishly choose to skip school. We were caught by the secretary of my high school and were punished by our parents, not by the school. One of the days after the incident my then friend choose to make a prank phone call from my house that I did not condone her doing. She threatened the secretary using the phone from my parent's house. I kicked her out and the next day I turned her in.

However, I was suspended for the rest of the year despite my not having any involvement other than that person using my phone. I was still able to graduate on time by attending another school. Since then, I have managed an impressive GPA in college, an internship with the Democratic National Convention Committee in the department of Communications and Public Affairs, joined a LGBTQ group called SPECTRUM at Central Piedmont Community College, and even joined Phi Theta Kappa Honor Society.

Please, let this mishap in no way affect your decision."

Thanks so much and I'm sorry it's so long!