According to the given description and findings, it would be correct to say that this is the Rovsing's sign.
The Rovsing's sign is the name given to the phenomenon of decreased or absent bowel sounds in a patient's right lower quadrant on palpation with deep left lower quadrant palpation. This is a sign of possible internal bleeding or inflammation in the right lower abdomen. This sign can be found in patients presenting with periumbilical abdominal pain, nausea, vomiting, and fever, as in the given scenario.