Core stabilization would not help you maintain good posture but maintaining a good posture would keep your core muscles in better shape. What you need is to maintain the right posture. Try to sit up tall and retract your neck so that the head just behind your spine. Like wise give a over correction of your lordosis and let go about 10 % to get your spine to the right lordosis. Do this atleast three times in a day about 15 repetitions. Many a times we underestimate the role of posture.
Asha