The most appropriate next step in management of this patient is to obtain an MRI of the right shoulder. This patient likely has an acute full-thickness tear of the right supraspinatus tendon, as suggested by her inability to abduct her right shoulder beyond 90 degrees, to lower her arm from 90 degrees of abduction (drop-arm test), and to maintain full external rotation when the arm is passively externally rotated at 20 degrees of abduction (external rotation lag test). To confirm the diagnosis in this patient, the most appropriate management would be to obtain a shoulder MRI, as it is a highly accurate and widely available modality for diagnosing full-thickness tears. Musculoskeletal ultrasonography is also highly sensitive for rotator cuff tears and may be used as a diagnostic study for suspected rotator cuff injuries. In the case of an acute full-thickness tear, immediate surgery is indicated.

Although glucocorticoid injection can lead to short-term pain improvement, the evidence for its use in rotator cuff tears is limited. Such injections may have a negative impact on healthy shoulder tendons, leading to worse surgical outcomes, and should therefore be avoided in patients who are potential surgical candidates.

Physical therapy alone would not be appropriate in this patient with a suspected complete rotator cuff tear who is a surgical candidate, as delayed orthopedic referral (>6 weeks) can lead to suboptimal surgical outcomes.

Although this patient has weakness on examination, she lacks other findings, such as paresthesias or pain in a dermatomal distribution, that suggest a nerve injury and might make a nerve conduction study helpful in diagnosis.