After the patient has used her epinephrine auto-injector, Sanjay should help her lie down because her heart rate is probably increasing, and it is important to keep her calm and in a position that can aid in circulation. He should continue to monitor her airway and watch for signs of nausea or vomiting, as these can occur during anaphylaxis. Since the patient is experiencing severe allergic reactions and has a swollen throat, it's crucial to administer high-flow oxygen to ensure adequate oxygenation.
In summary, the best approach would be to help her lie down, administer high-flow oxygen while observing for any changes in her condition, and be prepared to respond to any further deterioration.