Hi magisham, I have been on a wheat free diet and did me no harm. Mind you I don't have diabetes and not had kidney surgery. As jack has said there is plenty of dietary advice on the forum. Read and learn about the pros and cons and ask questions.
The one thing I did notice was the high reading the day after exercise. I still get this myself. It is not unusual. It is similar to a liver dump that your body thinks you need expecting you to do the same as the day before. Usually a 30 min walk will get your levels down again. If you are on a low carb diet, you don't need wheat products as you will get all the carbs you need from veg or fruit.