If you experience headaches that cause you vomit and huddle, then you are likely to suffer from migraines. You must be diagnosed correctly by the doctor. That's the only way you will know for sure that you have a migraine.
You have to go to an ordinary doctor first. Migraine is a very common misery that affects many in the world. This means that your doctor has probably had patients with migraine before. If your doctor will tell you to go to a more quality medical expert, then that's the time to see a specialist.
You can ask your doctor to refer you to a specialist. You also have to contact your local medical board for information. There are also many major headache organizations for professionals in the US. So there might be one near your area. You can go to these organizations to request names and specialist contact details.
Families and friends are also a good source of information when it comes to a doctor. You might know someone who also suffers from migraines so you can ask him about the specialist he saw. You can also get references from local teaching hospitals or universities. To filter the doctor correctly, you must ask them about their experience in treating headaches and the number of patients currently they have.