What term refers to severe pain that occurs with great intensity and has a sudden onset?

The term that describes severe pain occurring with great intensity and having a sudden onset is "acute." Acute pain is characterized by its sudden onset and can range in intensity from mild to severe. It usually indicates a specific injury or condition that requires immediate attention and is typically short-lived, often resolving with treatment or as the underlying cause is addressed.

"Fulminant," while it may suggest something severe or sudden, is generally used in medical contexts to describe a rapid and intense progression of a disease, rather than specifically referring to pain. "Chronic" denotes a long-lasting condition, typically persisting for months or years, which is the opposite of the acute presentation described in the question. "Exacerbated" refers to the worsening or flare-up of a pre-existing condition rather than the sudden onset of pain itself.

Therefore, acute is the most appropriate term for severe pain with a sudden onset.