Since tension headaches often come from muscle spasms, is it possible that doing dishes causes you a lot of stress for some reason? What are you thinking about while you do dishes?
I am not a doctor, but I know that although tension headaches can be treated naturally with meditative breathing and massage, they can be alleviated much more quickly with a mild muscle relaxer. Even though you are trying to live naturally, taking medicine for two or three days can get rid of those spasms (if that is what is causing it). Of course, they would have to be prescribed by a physician.
Also, are you sure that it is washing the dishes, or just a cooincidence?