Cold water is fine, but my tooth throbs when I drink hot soup.

A throbbing pain in response to heat is a warning sign you should not brush off. Sensitivity to cold can appear with early irritation, but pain triggered by heat is a pattern often seen once inflammation of the tooth nerve (pulp) has progressed considerably, and root canal treatment is frequently needed. Come in promptly in particular if 1) the pain lasts several minutes or more after something hot, 2) it throbs even at rest, or 3) it wakes you at night. If treatment is delayed the inflammation can spread to the bone at the root tip, so please have an examination even if the symptom has settled.