Final answer:
The nurse should immediately call the rapid response team due to the patient's symptoms indicating potential hemodynamic instability and the urgency of the situation given the patient's diagnosis of deep vein thrombosis.
Step-by-step explanation:
The nurse's first course of action should be to call the rapid response team. This is because the patient is showing signs of potential hemodynamic instability which may indicate a progression to a more serious condition, possibly pulmonary embolism, given the history of deep vein thrombosis and the current symptoms of tachycardia, tachypnea, hypotension, anxiety, and restlessness.
Administration of a sedative or eliciting a positive Homan's sign are not immediate priorities in the presence of potentially life-threatening symptoms, and increasing the flow rate of intravenous fluids without assessment by a rapid response team could be dangerous if heart function is compromised.
The patient's elevated heart rate (tachycardia), which is above 100 beats per minute for an adult at rest, is particularly concerning in this context and warrants urgent assessment and potential intervention by a multi-disciplinary team that can provide immediate and advanced medical care.