When a person has convulsions the convulsions are usually caused by seizures, reactions to medications, drug use etc.
Sometimes there are headaches related to some seizures which means that if you already have seizures and experience migraines then those migraines can lead to convulsions.
But the headaches are usually not the cause of the convulsions but in some cases it can.
Migraines and seizures both involve abnormal electrical activity in the brain so they are related but usually when you have convulsions it's caused by seizures, medication reactions, drug use such as meth etc.
When you have convulsions sometimes they will go away on their own without medical treatment but other times you need to seek medical attention for the convulsions.