I am having a headache does not sound natural. I have a headache is the usual way to express the idea.
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teacherJapan"I am having a headache"Speakers of Indian English might say this.
AnonymousI think with the right situation, it is correct. I am having the worst headache because my mother-in-law is coming to visit for a month and staying with us.That doesn't sound natural to me.
teacherJapanIs it better to use "I have a headache?"In the "neutral case", yes, but there are times when the continuous is fine.
CalifJimbut there are times when the continuous is fine.That's was my point. I am glad to see your approval.