From responses I have read on here from people eating low carb, different people respond in different ways to different foods.
I ate as low carb as I could until I saw my blood glucose numbers dropping to safe levels - I did not bother much about the protein and fat content as it was pretty obvious very quickly that eating fewer carbs is the key.
Having a meter so I could check that I was not going high after meals helped enormously.
I am really sensitive to carbs, so just a little bread or potato would raise my BG to double figures and it would stay there for hours. After a while I could eat a bit more and still see my numbers going down.
I started off eating only meat or fish for a day or so, then small amounts of salad and low carb veges, tiny amounts of fruit (frozen berries), until I was going dizzy from dropping blood glucose. That was only because I was getting down to normal levels, not going hypo, but that is what it felt like - as I was staggering about I ate just a few grapes to get rid of it, and had to do that several times, until I got used to having a BG level in single figures.
If you can measure your BG levels before eating and then two hours after, and see a rise of less than two whole numbers then that should be OK - as long as you are in single figures to start with.
Do eat fats - you don't want to train your body to break down proteins, as you have some essential parts which are made from protein, such as your heart, which really need to be safeguarded