Still receiving messages on my watch

This should sync across to your Apple Watch automatically and I would start by restarting both your iPhone and Apple Watch using the steps from these links:

Restart your iPhone, iPad, or iPod touch

How to restart your Apple Watch

Also, just to isolate the issue, make sure all your devices are completely up to date as well. These links can help you with updating your Apple Watch, and backing up and updating your iPhone:

Update your Apple Watch

How to back up your iPhone, iPad, and iPod touch

Update your iPhone, iPad, or iPod touch

If this doesn’t help, unpair your watch and iPhone. Pair them back together when this is done and see if the issue is resolved:

Unpair and erase your Apple Watch

Set up your Apple Watch

If you continue to have the issue after taking those steps, you can reach out to Apple Support using the following link to continue to look into this with you:

Contact Apple Support