How can a doctor tell the difference between hypoglycemia and hyperglycemia?

Sugar levels: Hypo- too low. Hyper- too high blood tests will tell you/ your doctor.

By measuring : By measuring blood glucose levels and a good medical history.

It's easy: As they are totally different and can be easily distinguished by blood testing. By the way, almost no one has hypoglycemia unless they are on diabetes medication, or have cancer, end stage renal or liver disease, or prior GI surgery. Hyperglycemia and diabetes, on the other hand, are far too common and getting more frequent each year.