Hi kishky,
For help with iPhone screen rotation keep in mind "Some apps don't support rotation, so your screen might not rotate even if Portrait Orientation Lock isn't turned on." You can find this information and other helpful details in the article here: Rotate the screen on your iPhone or iPod touch
However, if this is the built-in Messages app on your iPhone, and not a third-party message app test the steps below found in the same article.
"Rotate the screen on an iPhone without a Home button
- Swipe down from the top-right corner of your screen to open Control Center.
- Tap the Portrait Orientation Lock button
to make sure that it's off. - Turn your iPhone sideways.
If the screen still doesn't rotate, try a different app — like Safari or Messages — which are known to work in landscape mode.
Learn how to rotate the screen on your iPad.
"
If the issue continues, test force closing the app and completing a normal restart of your iPhone.
Close an app on your iPhone or iPod touch - Apple Support
Restart your iPhone - Apple Support
Hope the information helps.
Cheers.