Is it normal to have severe headaches after crying?

? migraine. Intense physical exertion can cause migraine headaches. If you are younger than 30 and have a family history of migraines this could be it. The headache pain is typically one-sided, is throbbing in nature, with associated nausea/vomiting. Light and sound sensitivity can also accompany. Classically there can be an aura before the onset - visual changes, pins/needles arm/leg, or speech problems.
Not really. Severe headaches could be related to a severe sinus congestion, or to a serious but rare condition such as cavernous sinus thrombosis. You should get this checked by a neurologist who specializes in headaches.