Could somoeone have both fibromalgia and parkinson's?

Yes: The two conditions have distinct pathophysiology and there is nothing about the one that would prevent the other. Lots of people have parkinsons and lots have fibromyalgia, just like lots of people have diabetes. Some people have parkinsons and diabetes, so too can they have parkinsons and fibromyalgia, the tricky part is having parkinsons might make diagnosis of fibromyalgia more difficult.

Parkinsons and Fibro: Although everything is possible, parkinson's itself may be manifested by fatigue, rigidity, dizziness, pains, and other symptoms which may be similar to the symptoms associsated with fibromyalgic syndromes.