Javaspeak - I sometimes get a frontal headache (top of the head and around the eyes) during and after Sirsasana (headstand), as I suffer with sinus problems (which may also apply to hayfever, allergy and cold sufferers) and obviously, they seem to object to having weight resting on them! This usually goes away after sleep and is never a "stabbing" pain, more a dull ache which makes the whole head feel heavy.
Is it caffeinated coffee that you drink and, do you normally drink coffee, apart from the days you practice? Do you have a similar reaction or is it purely limited to your practice? Some people react strongly to coffee, and as coffee already increases the blood pressure (temporarily until the caffeine wears off) within the body, it might be possible that the caffeine is affecting you adversely during the headstand. Perhaps trying to eat a small snack before practice/class instead of the coffee?
None of that may apply to you, but I thought I'd throw it in on the off-chance that it helps!
