Many internal and environmental triggers of primary headaches have been proposed, but establishing firm evidence for any of them has proved elusive. Geomagnetic storms, the disturbances of Earth's magnetic field following Solar eruptions, have been proposed as one such trigger. In this study, we utilized a vast amount of self-reported symptoms from the online social networking service Twitter in order to investigate a purported link between the level of geomagnetic activity and the onset of primary headaches and migraines. We analyzed 63 million keyword-bearing messages posted over the three years covering the maximum of Solar Cycle 24. No correlation has been found despite the large sample size. The simulation reveals that the significant correlation would have emerged even if only 1% of headache (2% of migraine) instances were caused by geomagnetic disturbances, thus placing very low upper limits on the prevalence of this trigger among Twitter users.