A: However justified, complaining to a manager about a colleague is seldom the best way to resolve problems. That's partly because of the commonly held contempt for sneaks and informers and at least as much because it puts managers in a difficult position. Managers are understandably reluctant to penalise worker A simply on the say-so of worker B.
By the sound of it, your job requires you to work in partnership with your panic-prone colleague. So I think you'd be perfectly entitled to ask for another partner on the grounds that you don't make a very productive pair. This allows for the fault to be as much yours as the other's.
If your manager thinks otherwise, that's his decision - not yours.