Should I have confronted her privately instead?

AITA for going through my fiance phone during her bachelorette party and exposing her in front of everyone. I know how bad that sounds. Just let me explain. We are getting married in three weeks. Everything was planned. The venue, the dress, the seating chart, all of it. Her best friend organized a bachelorette weekend at a lake house and invited me to drop off some decorations on the last night since I was already in the area for my own bachelor thing nearby. I figured I would say a quick hello and leave. When I got there the music was loud and everyone was drunk and happy. My fiance ran up and hugged me and her phone fell out of her pocket. It landed face up on the floor and a message popped up on the screen from a name saved as Work Mike. The message said I cannot stop thinking about last week, same place next Friday. I froze. She did not even notice the phone had fallen. I picked it up and my hands were shaking. I should have walked away and talked to her privately. I did not. I asked her in front of everyone who Work Mike was. She laughed it off at first and said he was just a coworker being weird. Then I read the message out loud. The entire room went silent. Her best friend covered her mouth. Another bridesmaid looked like she was going to be sick. That is when I knew they already suspected something. My fiance grabbed the phone from me and her face went white. She tried to pull me outside to talk privately but it was too late, everyone had already heard it. I asked her straight up if she was cheating. She said it was not what it sounded like. That is what they always say. I asked her to unlock the phone right there. She refused. I told her if she had nothing to hide she would show me. She started crying and said I was humiliating her in front of her friends. I said she humiliated herself months ago. Her best friend finally spoke up and said she had seen messages before but did not want to get involved. That broke me even more because it meant people already knew before I did. I left the lake house that night without another word. I drove two hours back to the city with my hands gripping the wheel so tight they hurt. She called sixteen times. I did not answer. The next morning she showed up at my apartment with red eyes and a folder of printed messages, trying to prove it was emotional only and never physical. I did not care about the technicality. She had been lying to my face for months while I was choosing flowers and writing vows. I told her the wedding was off. She begged, she promised it meant nothing, she said Work Mike was just someone who listened to her when she felt ignored by me. I asked since when did she feel ignored. She said since I started working late for overtime to pay for our wedding. That hit hard because I was literally working extra shifts to give her the wedding she wanted. Now her family is furious at me, not her. They are saying I embarrassed her publicly and should have handled it quietly instead of calling her out at her own party. Some of my friends agree with them. They say I should have waited and confronted her at home like an adult. Others say she deserved it because she was about to walk down the aisle to me while planning to meet another man the following week. Three weeks before our wedding and I found out my entire relationship was a lie, exposed by a dropped phone and one careless message. Was I wrong for exposing her right there in front of everyone instead of waiting until we were alone.