I can understand your concern. And your girlfriends anxiety. A panic attack has to be one of the most frightening things a person can endure. Those who have never experienced a true PANIC attack can never understand. Many people have felt anxiety in their lives, even extreme anxiety, and they then think they understand panic and couldn't be more wrong.
Having panic disorder or a chronic anxiety disorder CAN lead to a person becoming depressed, but it usually will not happen after one episode. And the paranoia your girlfriend is exhibiting is not normal at all for panic.
I am not a doctor nor a pharmacist and may be very wrong about this, but I have to wonder if propranolol was the best choice for one isolated panic attack. Some of the side effects of this medication are depression, hallucinations, vivid dreams and disorientation. She has apparently only been on this med for a few days but we are all different in how we react to medication. She could possibly be having an adverse reaction to it.
I would do everything in my power to get her into a psychiatrist as soon as possible. Panic attacks can and often do appear out of nowhere at any times in our lives, and that is "normal," The sudden onset of depression and paranoia, such as what your girlfriend experienced, is not normal and in my humble and non-medical opinion requires immediate intervention.
If she continues to show symptoms of depression and paranoia and you cannot get her in to see a psychiatrist now, I would take her to the ER.
I really don't mean to scare you, but as I said, the suddeness of these symptoms would concern me. It's always better to be safe than sorry.
You need to be really strong right now and I'm sure that wont be easy as I now how scared you must be as well.
Please let us know what they find out, OK?