No, Congress should not approve the use of military force in Syria, because there is disagreement as to whether we should be using force. There are a great deal of problems in the Middle East, and as much as it might be nice, the United States cannot act as the world's policeman. We cannot afford it.
Syria's chemical weapons were taken care of by an international agreement. Now, Congress should not authorize military force in Syria for any reason since the civil war is, by definition, an internal struggle between Bashar al-Assad and the rebels. The United States has very little interest in Syria, so we should stay out of the internal conflict as much as possible.