Acute Appendicitis: The patient's symptoms of severe abdominal pain, particularly in the right lower quadrant, fever, tachycardia, and positive McBurney and Psoas signs are highly suggestive of acute appendicitis. The progression of pain and the presence of guarding and rebound tenderness further support this diagnosis.

Mesenteric Lymphadenitis: This condition can mimic appendicitis and is often associated with viral infections. It could be considered if the patient has recently been ill or if appendicitis is ruled out.
Intestinal Obstruction: Although less likely given the acute onset, intestinal obstruction could cause severe abdominal pain, vomiting, and altered bowel habits. The presence of fever and tachycardia might suggest a complicated obstruction.
Gastroenteritis: Severe gastroenteritis could cause abdominal pain, fever, and tachycardia. However, the localized tenderness and specific signs like McBurney and Psoas signs are less typical for gastroenteritis.

Ectopic Pregnancy (in female patients, not applicable here): Although the patient is male, it's essential to remember this condition in female patients presenting with similar symptoms.
Perforated Viscus: Any condition leading to perforation of the gastrointestinal tract (e.g., perforated ulcer, typhoid fever) could present with severe abdominal pain, fever, and signs of peritonitis.
Intra-abdominal Shunt or Abscess: Complications of infections or surgeries could lead to abscess formation or shunt malfunction, presenting with severe abdominal pain and systemic signs of infection.

Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can present with abdominal pain, fever, and weight loss. While less likely to cause acute severe pain, they should be considered in the differential, especially if other diagnoses are ruled out.
Abdominal Malignancy: Although rare in children, abdominal tumors could cause pain, weight loss, and systemic symptoms. This would be a consideration if initial workup and treatment for more common conditions do not lead to improvement.
Ovarian Torsion (in female patients, not applicable here): Like ectopic pregnancy, ovarian torsion is a critical diagnosis to consider in female patients with acute abdominal pain, but it is not relevant to this male patient.