Hey Mrln999,
We understand the photos on your iPhone aren't syncing to iCloud. If your iPhone is connected to a cellular network, connect to a reliable Wi-Fi network. That way it isn't relying on your cellular data.
If you're having to use a cellular network, make sure Cellular Data is enabled in Settings > Photos > Cellular Data. Keep in mind, using cellular data will go towards your data plan that you have with your wireless carrier.
When the iPhone is not in use, make sure it is connected to a power source to ensure there's plenty of battery life.
Also, make sure Low Power Mode is disabled. Having it enabled will pause iCloud Photos. Fore more information about Low Power Mode, click here: Use Low Power Mode to save battery life on your iPhone or iPad.
Hope this helps. Take care.