Is this migranes?

It might seem odd to not know if I'm suffering from migraines, but here's my story. I've had all kinds of allergies all my life, mainly environmental allergies, with the worst being tobacco smoke (I've actually been skin tested more than once for tobacco, and it's off the charts bad), mold, cats, grass pollen, and some other pollen. If I was around a trigger, I'd be sick for a long time - typically with a sinus infection that would last at least two months.

Going gluten free has changed that. The sinus infections no longer occur and most allergies are significantly better, but I still have a strong reaction to artificial scent, which is more of a chemical sensitivity than an allergy in most cases. Tying tobacco for the worst reaction is artificial scent, it's that bad. Perfume and cologne tend to be the worst, but air fresheners and ambient scenting are almost as bad. I got sick on New Year's from a half hour in a mall with all kinds of artificial scents and ambient scenting. In the old days, I'd get a sinus infection, so I always blamed the headaches on that. But now, there's no sinus infection, but I still feel severely fatigued with massive headaches the next day, often on the left side, feeling like an arrow of pain is shooting from the temple to the back of the head. I also feel extremely achy. I've had two reactions in the past week like this from air fresheners in public washrooms - the next day is a total waste.

I also have a trigger from strobing lights, fast moving light, even watching a hockey game on TV is a problem if the camera moves too fast.

I'm kind of coming to a conclusion that migraines are an issue, although I'm going through more tests related to high ferritin levels and high liver enzymes, so I wonder how much connection is there. Anyway, I know these things can all be migraine triggers, but does a dull, throbbing headache - often a severe one but not always - match the description?

Thank you everyone!