Is there a low car diet I could go on that would help my frequent headaches?

Migraine diet. Several reviews use elimination diet like avoid chocolate, pizza, red wine, aspartame, nitrates like sausage, old cheese but low carb in a diabetic could produve some hypoglycemia symptoms, including headache.
Ketogenic Diet. If you search for ketogenic diet you may find some suggestions specific for headaches. This type diet is sometimes effective for treating headaches and epilepsy.