If you want to keep track of unread messages on Instagram, you can easily do so on your iPhone. First, open the Instagram app and sign in. Next, go to the main menu and select “Settings.” From here, scroll down until you see “Messages.” Tap it and then select “Unread Messages.” You’ll now see a list of all the unread messages on Instagram. To mark a message as read, just tap it and it will be added to your reading list. ..