Unsweetened Soya milk is really very low carb,the one I use is 1.0g of carbohydrate per 250ml.Just make sure it is unsweetened.Single cream is also great in coffee as it has virtually none of the sugars you will find in milk eg lactose.So both are good for low carbing.
I personally have had success low carbing as your doctor suggests.
I still find it remarkable that dieticians promote the NHS healthy plate which encourages starchy carbohydrate with every meal.Fine for everyone else but not for us diabetics who cannot process carbs or the glucose they produce.
According to my meter bread,rice,pasta and potato really don't help my BG levels.Ask your dietician about that and see what they have to say.