Penicillin-induced ataxia: This is a rare but recognized side effect of penicillin, particularly in elderly patients or those with renal impairment. The temporal relationship between penicillin administration and the onset of ataxia supports this diagnosis.

Vitamin B12 deficiency: This condition can cause ataxia and is more common in elderly patients, especially those with a history of gastrointestinal disorders or malabsorption. However, the acute onset after penicillin use makes this less likely.
CNS infection or abscess: Although the patient was prescribed penicillin for a sore throat, the development of ataxia could indicate a CNS infection, especially if the sore throat was a symptom of a more serious infection.
Medication interaction: The patient is on Xarelto, and while interactions with penicillin are not well-documented, the combination of medications could potentially contribute to ataxia through an unknown mechanism or by affecting renal function and thus drug clearance.

Stroke or cerebellar infarct: Although less likely given the context, a stroke could present with ataxia and must be considered due to the high risk of mortality and morbidity if missed. The patient's history of COPD and prior PE increases his cardiovascular risk.
Wernicke's encephalopathy: This is a medical emergency that can present with ataxia, among other symptoms. It is caused by thiamine deficiency and is more common in alcoholics but can occur in any condition leading to malnutrition.

Penicillin-induced seizures: While rare, penicillin can induce seizures, especially in patients with a history of seizure disorders or those with renal impairment. Ataxia could potentially be a post-ictal phenomenon.
Cerebellar degeneration: This is a progressive condition but could have an acute presentation in the context of another illness or medication use. However, this would be less likely given the acute onset after penicillin administration.