I have been drinking baking soda with lemon or lime for months now and have not had a problem--however, when I told my naturopathic doctor about it, he immediately checked my blood pressure and said that drinking baking soda can increase blood pressure. So that might be what is giving you headaches.
I would try adding the juice of one lemon or lime to 1/4 tsp baking soda and a half glass of water and see if that agrees with you better.