Not ideal. The regimen for patients with diabetes should control blood sugars adequately, so that first am (fasting) bgs are in the normal range, ideally 80-120. The timing of meds around this reading is less important than the reading itself which, if high, indicates a likely need for modification to diet, exercise, meds, or all three.
See md. This is exactly what you would address at a visit with your pcp or endocrinologist- bc an answer that would truly benefit you requires knowing a lot more information about you than is possible in this online format.
Need more specifics. Is the medicine insulin/ are you just about to eat? Are going to exercise before you eat.? Are your sugars usually "high" when you arise or is that an exception? What is a 'high' sugar? Do you count carbohydrates? When do you next check your blood sugar? If on Insulin fasting sugars less than 100 can be too low. Tell us more tell us more.