Hey MattR300,
I understand that you're not seeing edits that are made to notes you've shared from your iPhone.
First, if you haven't already, tap Settings > [your name] > iCloud > Notes, and disable Notes temporarily. Wait a moment, then re-enable the feature and test to see if edits are pushed through.
If edits still aren't updating, try switching network on the iPhone. This can rule out the issue being with the connection. For example, if you're connected to cellular data, try switching off cellular data and connecting to Wi-Fi only, or vice versa. If you're not sure how to turn off cellular data to connect to Wi-Fi only, follow these steps: Check the cellular data usage on your iPhone and iPad - Apple Support
I'd also recommend creating a new shared note and testing to see if the behavior is different. If you still can't see the edits, log in to iCloud.com and test to see if the edits are showing there.
Keep us updated.