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Of American-English origin, the noun ice-cream headache designates: severe but usually short-lived pain in the frontal or temporal region of the head, induced by the consumption of very cold food or drink or by other exposure to cold.

This noun occurs, for example, in the following from the column Dr Fred Kavalier Casebook, published in the Belfast Telegraph (Belfast, County Antrim, Northern Ireland) of Saturday 23^rd December 2006 [page 26, column 1]:

Ice cream makes my head hurt

Q—Whenever I drink more than a few sips of an ice-cold drink, I get a headache. It lasts for perhaps half a minute and  then goes away. The worst cause is a McDonald’s milkshake, which causes the headache after a few sips. Is there a cure for this?
A—The technical name for this is a cold stimulus headache, more commonly known as ice-cream headache. It is caused by cold liquids coming into contact with the palate and the back of the throat. It has been estimated that as many as 75% of people have had this problem at some time in their life. About three years ago, a group of Canadian 14-year-old school pupils published a research paper in the British Medical Journal about ice-cream headache. They discovered that if you eat ice-cream quickly, you are much more likely to get a headache than if you eat it slowly. Suggested cures include pressing your thumb up against the front of your palate—probably by raising the temperature of the palate. Another is to firmly massage both sides of the back of the neck.

I have found an early mention of headache induced by the consumption of ice cream in the following paragraph from The Saturday Republican (Louisiana, Missouri, USA) of Saturday 5^th April 1884 [page 3, column 2]:

Now that summer is coming on, we deem it our duty to inform the female portion of the community that ice-cream causes headache, indigestion, congestion of the liver. It will also make a fair complexioned girl break out with boils, pimples, warts and freckles. Boys give us five dollars for printing this.

These are, in chronological order, the earliest occurrences of the noun ice-cream headache that I have found:

1-: From the Fall River Daily Herald (Fall River, Massachusetts, USA) of Wednesday 8^th June 1892 [page 2, column 2]:

THE ICE-CREAM HEADACHE.
Bolting the Frozen Mixture Badly Affects the Facial Nerve.

During the scorching weather of July and August you often rush into an ice-cream saloon with the avowed intention of cooling your body to at least a few degrees below the melting point. If you are in a great hurry you are apt to make the first few spoonfuls of the cooling mixture rather large. This almost immediately gives you a violent pain in the temples, or somewhere in the region of the eyes. Why is this? Did you ever stop to think? asks a writer in the St. Louis Republic.
One who has studied the physiology of the case says that it is caused in the following manner: The frozen mixture, coming in contact with the nerves of the throat (the larynx, pharynx, etc.) temporarily paralyzes them. The sensation instantly shoots to the center of those nerves, which is in the brain, but finds there a side connection in the shape of the great facial nerve, which starts from in front of the ear and extends its branches over the sides of the face.
One branch of this facial nerve, extending across the temple, is a “nerve of sensation,” while the other branches are simply “nerves of motion,” utilized chiefly to govern the play of the mouth. This great facial nerve sidetracks the pain which proceeds from the chill, throwing it out along the nerve branch which traverses the temple, the pain being most agonizing at the points where the nerve branches.
If the irritation be extraordinary the “reflex” action which takes place may cause a violent pain in the eyeballs as well as in the temple, the eye pain being simply sympathetic. The person who rashly swallows great mouthfuls of frozen milk should remember that every time it comes in contact with the nerves of the throat the whole nervous system is injured to a greater or less extent.

2-: From The Sun (New York City, New York, USA) of Tuesday 14^th November 1893 [page 7, column 3]:

IT’S A WOMAN’S PARADISE.
OPPORTUNITIES FOR DISSIPATION AFFORDED BY THE CANDY SHOW.
For Many of the Gentler Sex It Means One Wild Round of Candy “Jags” and Chocolate Ice Cream Headaches—Some of the Pitfalls that are Laid for Unwary Men.

The candy carvival [sic] is in full swing just now at the Lenox Lyceum. It is booked for a three weeks’ run, and there is every indication of its complete success. The caramel girl gets a candy “jag” on every night and gets up with a chocolate-ice-cream headache every day.