As far as I know there is no way to see a record of the private messages that you have sent.
It is odd that the "How do you spell the word for the number 10 in English?" box did not appear. This should be directly below the box where you type your message - it is not something that appears after you press Send Message.
Is it possible that your browser autofilled that box so you didn't notice it? Or that you filled it in before typing your message and forgot?