Brief Answer:
Read below.

Detailed Answer:
I read your question carefully and I understand your concern.

The causes of unilateral headache may be many. For that reason it might be useful if you provided some more detail such as the since when has it started, precise distribution, duration (seconds, minutes, hours), frequency, triggering factors (such as chewing, certain drinks or foods, stress etc), accompanying symptoms such nausea and vomiting, lacrimation, nasal congestion, fever etc. It is these details which enable to at least try to differentiate one cause from the other.

In the absence of such info for the moment I will mention some of the most common causes of unilateral headache at your age.

One possibility is trigeminal neuralgia, pain in the trajectory of the trigeminal nerve which supplies half of the scalp and face, causing sharp pain, usually lasting for seconds, triggered by chewing or speaking.
Another possibility is dysfunction of the temporomandibular joint, the joint between the mandible and the skull, causing pain not only in the joint area but radiating in adjacent regions as well.
Temporal arteritis is another cause to be considered in any unilateral pain over the age of 60. It is a condition which is characterized by inflammation of blood vessels, causing pain along the temples when temporal artery is involved. Some blood tests for inflammation and direct palpation are necessary, as if untreated vision impairment may follow.

I remain at your disposal for other questions, but possibly providing some of the details I mentioned before.

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