I had nightmares about tornados 3 times a week for as long as I remember. Both my mom and grandmother were high anxiety about storms so it's not surprising as a kid I had terrifying dreams of funnel clouds every where. Lived through several tornados (grew up in Iowa where the sirens went off constantly spring and summer.
Now for the really crazy part: I stopped having nightmares about this after I watched the movie Twister! It was the damnedest thing. Must have been some kind of "exposure therapy". I am NOT recommending this to you!!!! I'm just mentioning it since it was so weird. A visit to a therapist who specializes in trauma recovery to discuss is not a bad idea, could help reduce your anxiety level a bit and reduce the frequency of the nightmares