Yes, it very well could be a migraine, and you should see a neurologist. However, I personally always prefer to start with my PCP, and let her refer me because she always refers me to top specialists. I trust her judgement very much.
Yes, it means an extra copay, but otherwise I'm just picking a name out of a list and who knows if I'm choosing someone appropriate. For example, neurologists can specialize in migraine, vertigo, seizure, movement disorders like parkinsons, dementia, etc. You want one who specializes in migraine because if you accidentally get one who major interest and expertise is in dementia, that person won't know the latest research on migraine. But you won't know this if you just look at a list of neurologists - you need someone on the inside who knows which neurologist does what. Hopefully your primary care doc is that person for you.
In the meantime, someone below had great advice - start a diary and keep track of foods and your menstrual cycle. These are triggers for many people, and a good doctor who knows about migraines will ask you to do this anyway, so get a head start now.