Is there a cure for ice pick headaches?

Depends on your def: Most headaches can be controlled, that is the frequency and severity of the headaches be dramatically decreased, with medication or other forms of treatment. While that's not a "cure, " per se, like you'd get from taking penicillin for strep throat, better is better, an with the right therapy some people have had their headaches stop or improve significantly. It's not "all or nothing.".

Yes: You could be having a headache disorder like cluster headache, migraines or hemicrania continua. Consult your neurologist or a pain specialist; these headaches can be optimally managed.

Maybe indomethacin: There is not so much a cure, but indomethacin is known to work well for these often enough. http://www.hopkinsmedicine.org/neurology_neurosurgery/centers_clinics/headache/conditions/primary_stabbing_headache.html