Inguinal Hernia: The symptoms of intermittent left groin pain that extends to the left testicle, described as a burning sensation, and aggravated by sneezing, are highly suggestive of an inguinal hernia. The fact that the pain is exacerbated by activities that increase intra-abdominal pressure, such as sneezing, further supports this diagnosis. A negative CT abdomen and pelvis does not rule out a hernia, especially if it is small or reducible.

Epididymitis: Inflammation of the epididymis can cause pain in the testicle and groin area. While the burning sensation and exacerbation with sneezing are less typical, epididymitis should be considered, especially if there are urinary symptoms or signs of infection.
Spermatocele or Epididymal Cyst: These conditions can cause a sensation of heaviness or discomfort in the testicle and groin area, which might be perceived as burning. However, they are less likely to cause pain that worsens with sneezing.
Groin Strain: A strain of the muscles in the groin area can cause pain that radiates to the testicle. The pain pattern and exacerbation with activities like sneezing could fit, although this is less common.

Testicular Torsion: Although the intermittent nature of the pain and the absence of more severe symptoms might make this less likely, testicular torsion is a medical emergency that requires prompt diagnosis and treatment. Any testicular pain should prompt consideration of this condition.
Appendicitis (with an atypical presentation): While the CT abdomen and pelvis was negative, appendicitis can occasionally present with atypical symptoms, including testicular pain if the appendix is located near the testicle. This diagnosis should be considered, especially if other symptoms such as fever, nausea, or vomiting are present.
Kidney Stone: A stone in the ureter can cause severe pain (renal colic) that might radiate to the groin. Although the burning sensation and specific exacerbation with sneezing are not typical, a kidney stone should be considered, especially if there are other urinary symptoms.

Varicocele: An enlargement of the veins within the scrotum can cause a sensation of heaviness or discomfort, which might be described as burning. However, varicoceles are typically not painful and are less likely to cause symptoms that worsen with sneezing.
Neurogenic Pain: Conditions affecting the nerves, such as neuropathy or nerve entrapment, can cause burning pain in the groin and testicle area. These diagnoses are less common and would typically require specific diagnostic testing for confirmation.
Referred Pain from Lumbar Disc Disease: In some cases, pain from the lower back can radiate to the groin and testicle area. This would be an unusual presentation for lumbar disc disease but could be considered if other symptoms such as back pain or sciatica are present.