Additional infor : i'm only 30 years old.
I could certainly see making a long-term plan to move to somewhere warmer. You say it "isn't an option." But what is your quality of life now, if you are "desperate?" If it is true that your symptoms have no cause, then find a way to not have to feel the symptoms. Don't just hang around in the coldest area of the country (besides Alaska) and be miserable for the rest of your life.
That said, it doesn't sound like you have addressed the problem completely from a medical point of view. You have basically had the usual tests from a general practitioner, who has shrugged and said oh well. It's a doctor's job to diagnose. I'd ask for a referral to a specialist or specialists. To find out which ones, I would research every condition and disease whose symptoms include sensitivity to cold, and knock down every single one on the list with testing from the appropriate specialist.
Also, if you are not exercising now, start. It will help with your circulation.
Are you also heat sensitive, or is it only cold?
Here is a list of sort of the top-ten conditions that can produce cold temperature intolerance in the body. (Take out the spaces between the letters.) What you have might not be on the list, but it's a place to start.
w w w . h e a l t h l i n e . c o m / s y m p t o m / c o l d - i n t o l e r a n c e