What does a barometric pressure headache feel like?

Feels like: An intense, throbbing pain, often one side of the head. The pain is often accompanied by symptoms like nausea, vomiting, sound and light sensitivity, and auras. Auras are changes in vision, speech, and other sensations. They occur before the migraine starts.

Why do I get headaches during storms?

During a storm, cold and warm air collide, creating an extreme difference in barometric (or air) pressure. This creates the elements of a thunderstorm, like wind and rain. The change in barometric pressure may be what triggers your headache, whether that is a migraine, tension-type headache, or a sinus headache.