Is it possible to treat a headache?

I suffer from headaches every day. I visited the hospital, but they told me it's tension headaches and to relax and not stress myself out... So I try not to be overly sensitive, but it's my personality, so I find it hard to do. Even when I take the medication prescribed by the neurologist, it only works for a while. I'm thinking of going to a traditional Korean medicine clinic to get acupuncture, but do you think it will be effective? I've never been before, so I'm a little scared. I'm not good at getting acupuncture. I want to live without headaches and have a clear, light mind...