Hi
Exercise is known to decrease insulin resistance AND use up the available glucose that is stored in muscles ready for use. Either of these things could be happening, and resulting in your shakiness after exercise.
The more insulin people have floating about in their blood stream, and using on a regular basis to deal with carb intake, then the more insulin resistance they may have, although there are other factors involved too - obesity, activity, medications and other medical conditions all factor in. We RHers usually produce a lot of insulin, so it makes sense that we may have insulin resistance. There are a few tried and tested ways to reduce insulin resistance, and exercise is probably the biggest and fastest one. Then come lowering carbs in food and fasting (which actually just means eating less regularly to allow insulin levels to drop a bit) and some medications can help too.
Insulin resistance can be tested. I am not aware that it is available on the NHS but some private companies are willing to do the test privately. A couple of members have done this recently. It involves sending off a blood sample. Insulin is stored in the pancreas ready for use, then released into the blood stream. There is a constant level of 'background' insulin that is always present. This is measured by the fasting insulin test. Then there is additional insulin released after food is eaten. The fasting insulin level is a useful gauge to assess how much insulin resistance we have going on, although it can vary depending on recent carb intake, exercise, etc.
Regarding your exercise affecting carb and insulin, the body holds stores of glucose in the form of glycogen in the liver and the large muscles, ready for action if needed. This is often referred to on the forum as a 'liver dump' where those glucose stores are released into the blood stream. It can happen when he have gone a while without food, or when we are stressed, or active enough for our blood glucose to drop a little. The body then thinks 'aha, I need to top up glucose levels' and dumps some glucose into the bloodstream. It is a milder version of what happens when we experience a hypo and our body sorts it out without us eating something.
So if you exercise enough that your muscles become less insulin resistant AND you burn up available glucose from your bloodstream in order to fuel those muscles, you may well experience lowered glucose levels, and even a liver dump to release more glucose to provide more fuel.
Some people 'carb load' before exercise to ensure they have enough glucose around. Personally, I find that pretty disastrous, since my RH trumps the carb loading, and I end up with a double whammy hypo. lol. Instead, I prefer to eat a proper low carb meal 2-3 hours before exercise so that the fats and proteins in the food drip feed energy throughout the exercise. I also carry slower release snacks like nut bars and dark chocolate (oooh the hardship!) rather than energy drinks or sweets, because the slower release is unlikely to trigger RH.
Mind you, when I am properly doing very low carb I can exercise for a long time on no food at all, because I am in ketosis, and my muscles just love running on ketones.
Hope that helps.