Hey DC1917,
Thanks for using Apple Support Communities! I understand your sent messages aren't displaying as expected.
To start, if you haven't already done so, restart your iPhone. A restart can resolve a variety of issues. Use the steps here: Restart your iPhone
Is this happening with all your conversations, only one? If this is only happening with one try deleting that conversation and starting a new one. Be sure to save any messages you don't want to lose prior to deleting the conversation.
If this is happening with all conversations we'd like to continue working with you. Can you let us know a bit more information? Some helpful information would be:
Are you seeing this behavior with both iMessage (blue) and text message (green) messages?
Did this behavior start after any recent changes or updates?
Thanks again, and have a great day!