I just had a cyst on my vocal cord removed Wednesday. On the side where the MD chipped my tooth my tongue is swollen and numb. Will the swelling go down and will I get feeling back? The doctor didn't mention any of that in my post op care.

Chipped tooth. The sharp edge may be cutting into your tongue causing the swelling and inflammation. It may be a simple fix... have your dentist take a look.
See your doctor. this is not normal, see your doctor to follow up.
Cyst. Yes. See your dentist to treat the chip with a smoothing out if it is small or a filling if it is large. Your tongue will return to normal after the irritation is gone.
Yes. Chances are a nerve was injured during the procedure but most of the time it does recover! Be patient..... Hope this helps Dr Z.