My photos aren't photo streaming from my phone to mylaptop even though it appears tobe turned on. Any thoughts appreciated.

Welcome to the Apple Community Susie.

1. Photostream only syncs photos over Wi-Fi, make sure you are connected to Wi-Fi to begin with.
2. Photostream only syncs when the camera app is closed, ensure it is closed.
3. Photostream only syncs when the battery is above 20%, try recharging the device

Try disabling photo stream on your device (settings > iCloud), restarting your device and then re-enabling photo stream.

Note: disabling photostream and re-enabling it will result in any photos that are currently in the photostream album on your device, that are older than 30 days old, not being added back.