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From the nature of pain, frequency (4-5 times a day) and duration (20-60 Min), I suspect cluster headache
in your case. You can discus about it with your physician.
Apart from that, it is better to rule out other causes of headache in following hierarchy:
-Pathology in ear, teeth, sinus
or eyes, specially infection
-Neurological cause: may need MRI for that.
Your treatment will depend on cause of headache. So get yourself evaluated for above causes.
I hope this information has been both informative and helpful for you.
Wish you Good Health.
Dr. Ashish Mittal