Postpartum Back Pain: This is a common condition in postpartum women, especially those who are breastfeeding. The physical strain of pregnancy, childbirth, and breastfeeding can lead to back pain. The fact that the pain is severe enough to cause spasm-like pain and lead to a fall after sneezing suggests a significant musculoskeletal component.

Musculoskeletal Strain: Given the recent history of childbirth and the physical demands of caring for a newborn, musculoskeletal strain is a plausible diagnosis. The sneezing incident could have exacerbated an existing strain, leading to severe pain and the fall.
Herniated Disk: The postpartum period can increase the risk of herniated disks due to the physical stresses of pregnancy and childbirth. The severe pain and spasm, especially triggered by a sudden movement like sneezing, could indicate a herniated disk.
Osteoporosis: Although less common in a 33-year-old, osteoporosis could be considered, especially if there were any risk factors during pregnancy, such as significant vitamin D deficiency or prolonged bed rest. However, this would be less likely without other supporting factors.

Spinal Epidural Abscess: Although rare, this condition is a medical emergency that requires prompt diagnosis and treatment. Back pain that is severe, especially if accompanied by fever, neurological deficits, or recent infection, should raise suspicion for this condition.
Cauda Equina Syndrome: This is a serious condition that requires immediate medical attention. Symptoms can include severe low back pain, bowel or bladder dysfunction, and neurological deficits in the lower limbs. The sudden onset of severe pain and a fall could potentially be related to this condition.
Osteonecrosis (Avascular Necrosis): This condition can occur postpartum, especially if there was any complication during pregnancy that affected blood flow. Severe back pain could be a presenting symptom, although it is less common.

Spinal Tumor: Although rare, spinal tumors can cause back pain and should be considered in the differential diagnosis, especially if the pain is persistent, severe, and not relieved by rest.
Paget's Disease of Bone: This condition can cause bone pain and is more common in older adults but could be considered in a differential diagnosis of back pain, especially if there are other systemic symptoms or a family history.