More information can change the answers you get on this question... depending on a1c or daily blood sugar counts and medications (metformin for example), ketones might be involved. Keto-diastix is one brand of cheap strips that will give general blood sugar counts and ketone levels. These use urine instead of blood. Experiment with those, record the info and then ask your doctor to explain anything needed about it... These strips shouldn't replace the finger pricking glucometers, though
When exercising, the body needs extra energy or fuel (in the form of glucose) for the exercising muscles. For short bursts of exercise, such as a quick sprint to catch the bus, the muscles and the liver can release stores of glucose for fuel. With continued moderate exercising, however, your muscles take up glucose at almost 20 times the normal rate. This lowers blood glucose levels.
However, intense exercise can have the opposite effect and actually increase your blood glucose levels. The body recognizes intense exercise as a stress and releases stress hormones that tells your body to increase available blood glucose to fuel your muscles. If your glucose levels exceed normal levels discuss with your doctor medication or medication adjustment.
Maybe you can experiment with time of day that you exercise, as well as intensity and duration to see the impact.
How high do they go?
Exercise will stimulate your liver to release sugar which affects your blood sugar levels.
However, exercise is still so good for you don't stop just because of that.