This is not like a peer-review in English class -- it's way too important for that. Seasoned Admissions Directors at Princeton will be reading your essay looking for glimpses of your “character.” You should always share your essay with the teacher's who are writing your recommendation letters, as Admissions Officers look for your teachers to reinforce and confirm the "character" projected in a student's essay. Successful applications have everything in sync.
If you don't want to share your essays with your teachers, you should show them to several adults in your life that you know, admire and respect (not your parents). Ask them: "Does this essay convey who I am?" "Does this sound like me?" That is really critical. Your essay should sound as if you are standing in front of an Admissions Director reading it out loud. I once heard Peter Johnson, an Admissions Director at Columbia, give this tip on essays: "Your essay should be so personal and specific that if it fell out of your backpack at school, and it didn't have your name on it, that if a classmate, who you knew you well, happened upon it laying on the hallway of your school, he or she should be able to read it, immediately know it was your essay and return it to you." Random strangers on the internet really can't provide that kind of feedback.
Best of luck to you!