Some people do get a dip in their blood sugar after eating if the insulin they release kicks in too fast and too hard, but hypoglycemia is a very over-diagnosed condition. Many people who claim low blood sugar are never shown to actually have low blood sugar levels.
There is a recognised condition of low blood pressure that follows eating, however, called postprandial hypotension. It's possible that this condition could be causing your symptoms.
Eating diverts blood to the digestive tract, and less is then available to the brain, muscles, and other organs. There are some folk whose adaptive mechanisms are less than optimal, and therefore they may feel faint, dizzy, or weak, or even fall.
As people get older so does their vascular system, and its adaptability declines. There are things you can do to help, though:
Regular exercise tones your vascular system as well as your muscles, making it more able to cope with shifting requirements in different tissues, so walk for 30 minutes daily.
Drink one to two glasses of water 15 to 30 minutes before eating. This will increase the fluid in the blood and reduce the tendency for the blood pressure to fall after the meal.
Eat less than you may be doing now, and eat more slowly. Spreading a meal over a longer time interval will help you to feel satisfied after 15 to 20 minutes, so you will eat less and allow more time for digestion.
Although 2 meals a day reduces the post-meal metabolic stress we experience, some people benefit from smaller, more frequent meals.
Watch the type of carbohydrates you are eating. Food made with refined flour and refined sugar such as cakes, white bread, doughnuts and sweetened beverages, etc., and even white rice and potatoes cause a rapid increase in absorption with a greater tendency to postprandial low blood pressure. Eat more whole-grain products, legumes, healthful oils, and proteins.
Low blood pressure after a meal levels off after 30 minutes to an hour, so rest a little. Sit or lie down for a short break. Many people find they work better, have improved mental function, are are more productive after a 15- to 20-minute nap.
More importantly, discuss this issue with your doctor, he or she may find there is something specific that you as an individual need to do.