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I am getting porcelean caps on my front teeth and one of the temporary caps fell off last night. Would the exposed nerve cause me to me sick to my stomach and dizzy?

I don't think the exposed nerve will cause you to get sick and dizzy. If anything you may be allergic to the temporary cement they used to cement your crowns. Ask your dentist just for your future reference. I've never known anyone to be allergic to the cement though but I couldn't think of anything else that might've caused it.