To see messages you’ve sent with Instagram Direct, tap the 'paper aeroplane' in the top-right corner of Feed. From there you can manage the messages you’ve sent and received.
When you send a post from your newsfeed using Instagram Direct, it'll only visible to people who can already see it. For example, if you send a post from a private account as a message, only people who follow that account will be able to see it. Photos or videos sent with Instagram Direct can't be shared through Instagram to other sites like Facebook or Twitter, and won't appear on hashtag and location pages.