Final answer:
Considering the woman's difficulty breathing and history of type 2 diabetes and DVT, an EMT should suspect a pulmonary embolism.
Step-by-step explanation:
Based on the 66-year-old woman's sudden onset of difficulty breathing and her history of type 2 diabetes and deep vein thrombosis (DVT), the Emergency Medical Technician (EMT) should suspect pulmonary embolism (PE). This is because DVT can lead to PE, which is a condition where a blood clot breaks off and travels to the pulmonary arteries, causing serious blockages that can impair breathing and be life-threatening. The diagnosis of severe hypoglycemia, diabetic ketoacidosis, or congestive heart failure, although possible, seem less likely given the sudden nature of her symptoms and her specific history.