Hello dulljunkandstuff,
Thank you for using Apple Support Communities! I understand that you're seeing a loading icon below a recently sent message in the Messages app on your iPhone, and new messages sent to this contact do not appear. You've come to the right place for a resolution.
Let's start by forcing the Messages app to close, then check if the loading icon still appears:
How to force an app to close on your iPhone, iPad, or iPod touch - Apple Support
If there's no change, the following support article provides suggestions that I would like to have you try next. Be sure to start with the "Try these steps first" section. Based on the screenshot, your last message was sent as a SMS or MMS instead of an iMessage so you'll also want to check out the suggestions under the "If you see a green message bubble" section:
If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support
If you're still experiencing the issue, some additional information that may be helpful to know is: Can you send and receive messages with other contacts? If so, are they iMessages or SMS/MMS?
Cheers!