Even if the prescription in legitimate, the police can charge you and hold you until they verify it's your prescription. Most won't. My wife keeps a number of prescription medications in a pill organizer, but carries the papers from the pharmacy with her. That way, she has proof they're hers without carrying a myriad of brown bottles with her, and without announcing to the whole world what she's taking.
As long as your friend can produce the pharmacy paperwork and/or a note from the prescribing physician, the public defender should be more than adequate.