Kidney Stone: The combination of severe pain, often radiating to the back, and vomiting, especially after a bowel movement, is highly suggestive of a kidney stone. The pain can sometimes be referred to the testicle due to shared nerve roots.

Testicular Torsion: Although less likely given the back pain and vomiting, testicular torsion is a painful condition that requires urgent attention. It typically presents with acute testicular pain and may be accompanied by nausea and vomiting.
Epididymitis: Inflammation of the epididymis can cause testicular pain, which may radiate to the back, and can be accompanied by nausea and vomiting, especially if there is an associated infection.
Prostatitis: Inflammation of the prostate can cause lower back pain, testicular pain, and systemic symptoms like nausea and vomiting.

Appendicitis: Although the pain typically starts near the belly button and then moves to the lower right abdomen, atypical presentations can occur, and the vomiting could be a sign of peritonitis. Missing appendicitis can lead to severe complications.
Ruptured Abdominal Aortic Aneurysm: This is a life-threatening condition that can present with back pain and abdominal pain, and while less likely, it's crucial not to miss it due to its high mortality rate.
Testicular Cancer with Metastasis: While rare, testicular cancer can present with back pain due to metastasis and should not be overlooked, especially in younger men.

Potts Disease (Spinal Tuberculosis): Can cause back pain and, in rare cases, may refer pain to the testicles due to nerve involvement.
Referred Pain from Other Sources: Such as a peptic ulcer or pancreatitis, which can cause back pain and vomiting, though these would typically have other distinguishing symptoms.