No, they are used in different contexts. People shiver with cold, anxiety, fear, etc.; it is a continuous action of repeated shaking. An animal or a plant could quiver i.e. shake, possibly just once, in response to some stimulus or disturbance.

Thank you, Gray.

Adrian is right, although to tell the truth, they often CAN be used interchangeably. "Shiver" is usually a continuous action, but sometimes you may read something like "a shiver went through him," which is the same as a quiver -- a brief moment of shaking slightly. And even though "shiver" is the word most commonly associated with cold, you may also sometimes read about someone "quivering" from the cold. I would say that in literary language, they're more often interchangeable. In everyday conversation, "shivering" is continuous, and a "quiver" is brief.

You shiver from the cold or sometimes fear. Quiver can be more general or from emotions.