Sorry, I went back and tried to find perhaps an article or something to help you out. The best thing I could find that tried to keep things simple is:
http://en.wikipedia.org/wiki/Reactive_hypoglycemia
This article refers to reactive hypoglycemia (a type of postprandial hypoglycemia), so perhaps not all the symptoms apply to you. However, what causes the low blood sugar is essentially the same. Also, there are tips on what you can do to decrease your symptoms...you should try the things listed there to see if they help. If they do, then blood glucose testing to find out what's going on is definitely something you and your doctor should discuss.
What you are describing sounds like postprandial hypoglycemia. I disagree with the previous person's post about blood being shunted away from the brain and to your stomach. Even if this was a normal physiological response, it is very minor and should NOT make you feel dizzy or lightheaded.
During meals a set of signals will modulate how much insulin is released into your bloodstream (it depends on the composition of the food). If you are eating a high-carb meal, obviously more insulin will be secreted by the pancreas to help remove the glucose from the bloodstream once it is absorbed by the intestines. Occassionally the body will overshoot the amount of insulin secretion and you will actually remove too much glucose from your blood. Once your body realizes this, it will decrease insulin secretion and increase glucagon secretion, which will help stabilize your blood glucose levels.
Random glucose testing will typically not detect this type of problem, since you only experience symptoms after eating. If this is a continuous problem, a blood glucose test both before and after a meal is a good place to start. If the problem is due to too much insulin after a meal, you would expect low levels of glucose since the insulin is removing too much glucose from the blood.
This can occur because your blood goes to your stomach to digest the food and away from your brain. It's happened to me a few times. You can also develop postprandial hypotension. Falling blood pressure after eating. Try taking your blood pressure when you feel like this. It's probably low. Eat smaller meals higher in protein and do not excercise or exert yourself after meals.