Strangulated Hernia with Loops: This diagnosis is the most likely due to the presence of a tender umbilical mass, fever, redness, and audible intestinal sounds. Strangulation of a hernia occurs when the blood supply to the herniated tissue is cut off, leading to tissue death. The symptoms and signs presented are classic for this condition, which is a surgical emergency.

Strangulated Omentum: This condition involves the omentum (a layer of tissue that supports the intestines) becoming trapped and losing its blood supply. While it can present similarly to a strangulated hernia, the absence of a clear hernia sac makes it slightly less likely but still a consideration.
Obstructed Hernia with Loops: An obstructed hernia occurs when part of the intestine becomes trapped in the hernia and is unable to move back into the abdominal cavity, which can lead to bowel obstruction. This condition can also present with similar symptoms but might not always have the same level of urgency as a strangulated hernia unless it progresses to strangulation.

Appendicitis: Although the location is atypical for appendicitis (which usually presents with pain in the lower right abdomen), an inflamed appendix can sometimes be found in unusual locations, including near the umbilicus, especially if it's a retrocecal appendix. Missing appendicitis can lead to perforation and severe complications.
Intra-abdominal Abscess: An abscess in the abdominal cavity can present with fever, abdominal pain, and sometimes a palpable mass. It's crucial to consider this diagnosis, especially if there's a history of recent abdominal surgery, infection, or other conditions that could lead to abscess formation.

Desmoid Tumor: A desmoid tumor is a rare, benign tumor that can occur in the abdominal wall and present as a mass. While it doesn't typically cause acute symptoms like fever and redness, it's a consideration in the differential diagnosis for an umbilical mass.
Lymphoma: Certain types of lymphoma can present with abdominal masses and systemic symptoms like fever. Although rare, lymphoma should be considered, especially if other symptoms or findings suggestive of lymphoma are present.