Liz-
They (corn and peas) are high carb and spike your insulin level the same as potatoes, carrots, beets, lima beans, pasta, bread, sugar, etc. You are probably better off to stick to low carb veggies and lean meats and if you choose to have some higher carb veggies then have them in place of potatoes, bread, pasta, etc. Count the higher carb veggies as a 'carb' not 'veggie'.
Lower carb veggies would include - zuchinni, cabbage, salad greens, green beans, wax beans, broccoli, cauliflower, etc.