Hi James,
Welcome to Apple Support Communities. We understand that you're having an issue with selecting text on your iPhone. We'd like to help.
When do you notice this issue happening? Sometimes knowing if it's a specific app can help you isolate this issue quickly.
If it's does appear to be the same app each time, these steps can help you troubleshoot it:
If an app on your iPhone or iPad doesn't work as expected, try this.
1. Close and reopen the app
Force the app to close. Then open the app to see if it works as expected.
2. Restart your device
Restart your iPhone or restart your iPad. Then open the app to see if it works as expected.
3. Check for updates
To see if updates are available for the app, open the App Store, tap your profile icon, then scroll down to see if updates are available. If updates aren't available for the app, update the software on your iPhone or iPad.
4. Delete the app, then redownload it
Delete the app. When you do this, you might lose data that was stored in the app. Then redownload the app. Then check to see if the problem with the app is fixed.
Get more help
* If the App Store itself is not responding, contact Apple Support for your iPhone or for your iPad.
* If you found the app on the App Store, contact the app developer. If the app is made by Apple or came with your iPhone or iPad, contact Apple Support for your iPhone or for your iPad.
* If you bought the app recently and you no longer want it, you can also request a refund.
These steps can also be done if you notice it on a couple apps but if it's more widespread, it may be an issue that needs to be looked at further.
Let us know if that helps and we'll continue to help from here.
Cheers!