Acute Appendicitis: The patient's symptoms of severe abdominal pain, particularly in the right lower quadrant, along with 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, presenting with abdominal pain, fever, and similar physical examination findings. It is often related to viral infections and can be a consideration if appendicitis is ruled out.
Intestinal Obstruction: Although less likely given the acute onset and specific location of pain, intestinal obstruction could present with severe abdominal pain, vomiting, and altered bowel habits. The presence of fever and tachycardia might suggest a complicated obstruction.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis can present with chronic or acute abdominal pain, fever, and changes in bowel habits. The severity of symptoms and the presence of systemic signs like fever and tachycardia could suggest an acute flare of IBD.

Ectopic Pregnancy (in female patients, but included for completeness): Although the patient is male, it's essential to remember this critical diagnosis in female patients presenting with similar symptoms. In males, testicular torsion could be considered but typically presents with acute scrotal pain rather than abdominal pain.
Perforated Viscus: Any condition leading to the perforation of an abdominal organ (e.g., perforated ulcer, typhoid fever) can present with severe abdominal pain, fever, and signs of peritonitis. This is a surgical emergency.
Hemorrhagic Ovarian Cyst (in female patients): Again, while the patient is male, this is another condition that could present with acute abdominal pain and should be considered in female patients.

Yersinia Ileitis: A rare cause of abdominal pain that can mimic appendicitis, often associated with exposure to contaminated food or water.
Omental Torsion: A rare condition where the omentum twists, cutting off its blood supply, leading to severe abdominal pain.
Abdominal Malignancies: Although extremely rare in children, certain abdominal tumors could present with abdominal pain, fever, and systemic symptoms.