It sounds a little unnatural. If you still have a headache, I would say: "I've had a headache all day (today)". If the headache went away, I would say: "I had a headache today". *You can put today at the beginning of the sentence, but to me it sounds better at the end.

It's almost there! Just a small tweak for correct grammar: "Today, I have a headache." Or, if the headache has already passed: "Today, I had a headache."