There are three types of headaches. It comes and goes, waxes and wanes. The second most common is the migraine headache. Yes, little children do get migraines. They typically come, are there for a period of time, then go away.
Migraines come and go.
The third type, which is very rare luckily, is an organic headache. This is where something is growing inside the head causing pressure and pain. These are typically observed in the morning upon wakening. There may be morning vomiting, and they steadily and progressively get worse. What many doctors call a milk allergy is more of an intolerance, typically with vomiting and diarrhea.