Intense short headaches are frequently referred to as ice pick headaches, although the proper medical term is primary stabbing headache. These most often often occur as a part of a larger headache syndrome, and most often associated with migraine headaches. However, they can occur with other types of headaches.
Since they are of such short duration, it is usually difficult to treat these headaches with a medicine designed to relieve the headache, so the treatment is usually oriented towards that larger headache syndrome with which they are associated.
If you do not have migraine headaches or other vascular headaches, the doctor may have tried the beta-blocker to cover for the most common associated headache syndrome. Since the beta-blocker is not helping, then the next step would be to try an alternative preventive medicine.
It is true that sinus disease can cause chronic headaches, although only infrequently associated with ice pick headaches. But since you have rhinitis and an association of headaches with the need to sneeze, it would be appropriate to consider further evaluation or treatment by an ENT physician.
Another common headache syndrome are muscle contraction headaches. Ice pick headaches can be associated with muscle contraction headaches, although not as often as with migraine headaches. Sneezing can make muscle contraction headaches worse, but it is usually with the sneeze, rather than preceding the sneeze.
It would be reasonable to discuss with your doctor about the use of medicines to prevent muscle contraction headaches, such as amitriptyline or duloxetine. These are antidepressant medicines, but have also been shown to be effective at preventing a variety of chronic pain syndromes, including muscle contraction headaches, and it may help prevent any associated ice pick headaches.
If I can provide any additional information, please let me know.