Hello Dave M!,
To help us get a better understanding of the issue, we’d like to ask a few questions.
1. Does this only happen in the Messages app, or do you experience similar issues with scrolling in other apps as well?
2. When did you first notice this behavior? Were any changes made to your device or its settings before this began?
3. Do you experience the same behavior after restarting your device? We ask because restarting can correct some issues. This link explains how to restart: Restart your iPhone
How to restart your iPhone X, 11, 12, 13, or later
1. Press and hold either volume button and the side button until the power-off slider appears.

2. Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3. To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo.
Please let us know the outcome after giving the above steps a try.
Thanks for using the Apple Support Communities.
Cheers!