You should really try NOT to constantly eat, as this will be causing your poor pancreas to work overtime producing insulin to handle the continuous flow of glucose those snacks will be generating.
When you eat a low carb high(er) fat diet, you are replacing most of the quick short term energy you get from carbs with a steady more constant source from the fats, and as a result you should stop feeling hungry all the time.
With pre and post meal testing the idea is to see 2 hours after your meal what increase in glucose there has been from you pre meal level, and this should help you to determine your reaction to different types and quantities of carbohydrates, so you can adjust your diet accordingly. Quite honestly I don't know how often or when you should test if constantly snacking, or what useful information you might gain from doing so. But if you must, it may be better to use a continuous Libre sensor which will record your levels 24/7.