Hey there BarbedTexas,
We wanted to help by learning more about what's happening, along with ruling out some general possible causes:
- You mentioned that this occurs upon connecting your two devices together, but if you've been able to sync photos to the same Mac in the past, when did this start?
- Sometimes unexpected behavior can be resolved with a restart: Restart your iPhone and check out the section ‘Restart your Mac' here: Shut down or restart your Mac
- Since you have a compatible iPhone model, the latest version is iOS 16.4. You can verify this within Settings > General > About. In case you needed it, this link shows how to first back up, then Update your iPhone or iPad.
- If you have a compatible Mac model, the latest version is macOS 13.3. You can verify this by clicking on the Apple logo at the top left corner of the screen, then on ‘About This Mac’. In case you needed it, this link shows how to first back up, then Update macOS on Mac.
You mention that the "Trust this Computer" messages keeps flashing and this could be and issue with the port on the Mac, so make sure you test all the ports and test different cables. After that, please make sure you have followed these steps from the Apple resource on this:
"If you need help with the alert message
If you tap Trust or Don't Trust, but your computer doesn't accept your answer, or if the alert message won't appear, follow these steps. Try again after each.
1. Make sure that your computer has the latest version of macOS or the latest version of iTunes. If you downloaded iTunes for Windows from the Microsoft Store, make sure that iTunes Mobile Device Helper is enabled as a startup item.
2. Disconnect and reconnect your device from your computer.
3. Restart your computer.
4. Restart your iPhone, iPad, or iPod touch.
5. Reset your Location & Privacy settings.
6. Reset your Network settings. Go to Settings > General > Transfer or Reset [Device] > Reset and tap Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before.

Get more help
Learn what to do if your computer doesn't recognize your iPhone or iPad.
If you still need help, contact Apple Support."
And that is from About the 'Trust This Computer' alert message on your iPhone, iPad, or iPod touch - Apple Support
Cheers!