A corticosteroid or cortisone shot can cause a side effect of high blood sugar levels in people with diabetes. In most cases, this effect lasts several days.t is appropriate to check your blood sugar using a glucometer and test strips more often after you receive a medication that could alter your sugar. Several other medications can affect blood sugar. The drugs that are more likely to raise blood sugar levels include: 1  Prednisone or other corticosteroid pills.