Might want to go for an eye exam.
What am I going to say to the doctor? I have no problem with non-polarized sunglasses.
I have a long history of bad migraine. That is maybe the factor.
Tell him or her exactly that. You have eye strain with polarized sunglasses, but not without, and you have a history of migraine. Are these things related and can I just get my vision checked?
You don't really have to have something wrong to get your eyes checked. I'm talking about just a standard eye exam. Lots of places like Lens Crafters have eye doctors (optometrist, ophthalmologist...whatever it is) in the store for exams. Your difficulty with polarized glasses might be related to changes in your vision or an astigmatism or something. An eye exam will just give you more information and the opportunity to talk to someone who knows a lot more about vision than a bunch of yahoos on a photo forum