Epididymitis: This condition, often caused by bacterial infection (such as Chlamydia or Gonorrhea), can lead to symptoms like testicular pain, fever, and potentially blood in semen if the infection spreads. The sore throat could be a coincidental viral infection but also raises the possibility of a systemic infection.

Urethritis: Similar to epididymitis, urethritis (inflammation of the urethra) can be caused by sexually transmitted infections (STIs) and could explain the blood in semen and testicular pain. Fever and sore throat might accompany a systemic response to infection.
Orchitis: Inflammation of one or both testicles, usually caused by bacterial or viral infections, can lead to testicular pain, fever, and potentially blood in semen if there's associated epididymitis or urethritis. Mumps orchitis is a specific consideration if the sore throat is part of a viral syndrome.
Prostatitis: Inflammation of the prostate gland can cause testicular pain, fever, and potentially blood in semen. While less directly linked to sore throat, it remains a consideration in the differential for genitourinary symptoms.

Testicular Torsion: A medical emergency that requires immediate attention. While it primarily presents with sudden, severe testicular pain, it could be accompanied by fever and other systemic symptoms if there's associated infection or necrosis. Blood in semen might not be a primary symptom but could occur in severe cases.
Septicemia or Systemic Infection: Any severe infection (including those causing sore throat, like streptococcal infections) can lead to systemic symptoms including fever and potentially affect other systems, leading to the other symptoms mentioned.

Henoch-Schönlein Purpura (HSP): A form of vasculitis that can cause a variety of symptoms including joint pain, skin rash, and gastrointestinal symptoms. Rarely, it can cause testicular pain and potentially other genitourinary symptoms, though this would be an uncommon presentation.
Behçet's Disease: A rare condition that causes blood vessel inflammation throughout the body, leading to a wide range of symptoms including oral and genital ulcers, skin lesions, and eye inflammation. It could potentially cause some of the symptoms listed, though it would be a rare and less likely diagnosis.