Question

During an unscheduled visit to a primary care clinic, a 62-year-old retired teacher reports a 3-day history of progressively worsening shortness of breath and a persistent cough. He notes that his sputum has changed from clear to thick and yellow-green over the past 48 hours. His past medical history is significant for chronic obstructive pulmonary disease (COPD), heart failure with preserved ejection fraction (HFpEF), and Hashimoto thyroiditis. His current medications include inhaled tiotropium, oral metoprolol, and oral levothyroxine.

Vital signs are: temperature $37.9^\circ\text{C}$ ($100.2^\circ\text{F}$), blood pressure $138/86 \text{ mmHg}$, pulse $98/\text{min}$, and respirations $24/\text{min}$. Oxygen saturation is $89\%$ on room air.

Physical examination reveals a patient in mild respiratory distress. Lung auscultation demonstrates a prolonged expiratory phase with diffuse bilateral wheezing. Cardiac auscultation reveals a regular rhythm with normal heart sounds; there is no jugular venous distention and no peripheral edema.

Arterial blood gas analysis on room air reveals:
pH: $7.34$
PaCO $_2$: $54 \text{ mmHg}$
PaO $_2$: $60 \text{ mmHg}$
HCO $_3^-$: $28 \text{ mEq/L}$

Laboratory studies show a leukocyte count of $11,200/\text{mm}^3$, a thyroid-stimulating hormone (TSH) level of $3.5 \text{ \mu U/mL}$ (normal: $0.5-5.0 \text{ \mu U/mL}$), and a free T4 of $1.1 \text{ ng/dL}$ (normal: $0.8-1.8 \text{ ng/dL}$).

A chest radiograph displays hyperinflated lungs with flattened diaphragms, but no focal consolidation or pleural effusion.

Which of the following is the most appropriate next step in the management of this patient?