Can corticosteroid injections for nld in your leg cause your mouth to parch?

Yes: If by nld you mean necrobiosis lipoidica diabeticorum. It's possible that you are receiving too much corticosteroid. If that is the case your blood sugar may no longer be in control. This would result in increased polyuria, dehydration, and a parched mouth. Check your blood sugar and adjust your Insulin dose appropriately. Obviously you should check in with your diabetes specialist.