Final answer:
The patient exhibiting dyspnea, cyanosis of the lips, and cramping of the right calf muscle likely has a pulmonary embolism, which is a blockage in the pulmonary arteries usually caused by a dislodged deep vein thrombosis.
Step-by-step explanation:
Based on the symptoms of dyspnea, cyanosis of lips, and cramping of the right calf muscle in a patient with a tracheostomy tube, the physical therapist should suspect pulmonary embolism (PE). These symptoms are indicative of a potential blockage in the pulmonary arteries, which can stem from a deep vein thrombosis (DVT) that has dislodged and traveled to the lungs. This is a medical emergency and requires immediate attention. While conditions such as heart failure and respiratory distress may also present with similar symptoms like dyspnea, the combination of respiratory distress with a cramping calf muscle strongly suggests a venous thromboembolic event, making pulmonary embolism the most likely diagnosis.