But if you need it, you need it. The
jury duty part is, yes, you can get out of
jury duty due to
anxiety. Whether or not you need a doctor's note depends on your local jurisdiction, but you probably will. I would caution, though, that although you mention you're suffering anxiety because of this, you don't say how badly this is affecting your life in the sense of avoiding things. I know this is easy to say, but avoidance will make the problem harder to get over.