The simple fact that you have gestational diabetes puts you at much higher risk for developing type 2 diabetes after the baby's birth. Type 2 is non-insulin dependent diabetes and is usually controlled initially either through diet or through oral medications (vs. insulin injections).
I'd check with your OB. You should have been referred to an Endocrinologist to monitor your diabetes. Your local hospital system should also have a Certified Diabetes Educator (usually a nurse, dietician or pharmacist who has undergone extensive training and certification). Call and ask them what they recommend.
Having been involved in the world of Diabetes most of my career, I'd be very surprised if they didn't monitor your blood glucose levels more acutely than a non-gestational patient.
Regardless, you're at much higher risk, and once you have type 2 diabetes, it never goes away no matter how well it's controlled. I'd be very proactive in getting answers and making sure you're on top of it.
Good luck with the baby.