I'm going to tell people what someone in my class keeps sending me texts
Are you close to this person? Have you spoken to them about it?
I'm not close to this person.
It's okay to let people know if you don't want to have private conversations with them. This may upset them but its still your right. Try letting them down gently to not hurt them as badly.
I'll try my best, but I think this will go ugly.
Even though you're within your rights to make your conversations public, you should at least let the other person know about it. It's invasion of their privacy to show their texts to others. Nobody would trust you if you continued doing so.