The prescription event does not take up much storage and could probably be compressed and printed out as a QR and handed to the patient.

Or saved as a file on his phone/health insurance smart card.

To avoid double spends of the prescription, the optician or pharmacist could comment "dispensed" under the prescription event and publish to as many relays as he likes. Or better yet: publish an event of a new kind with the "dispensed" or "partially dispensed" tag and the prescription's event ID. That way the original prescription event never has to be published and patient data remains private.

But before dispensing the optician/pharmacist could look up the prescription's note ID for any dispensed events on any relay.

Double spends of drug prescription would be fixed, patient data never leaves the patients phone/health insurance card and could even work offline (except for the double spend protection if the pharmacist is offline too).