Can Botox Permanently Damage Your Actual Eye Muscles and Optical Nerves?

It is highly unlikely that the botox caused intraocular muscle problems although it is possible.  The effects will wear off , but you should check back with your doctor regularly.

I have NEVER heard of a case where Botox to the FRONTALIS (forehead muscles) and Crow's feet areas (lateral orbicularis oculi muscles) have paralyzed the eye muscles or optic nerves.
To do so would require an intra-orbital (inside the eye socket) injection as USED TO BE DONE for one of Botox's earliest indications when it came out as a treatment of spastic disorders including those involving the inner eye muscles.
The MOST common explanation is an over-paralysis of the forehead muscles unveiling a significant drooping of the brows (which until now were held upright ONLY by the upward Frontalis pull). AND / OR migration of the Botox to paralyze the LEVATOR muscle of the upper lid causing a droopy eyelid. This latter complication can be caused by rubbing the Botox into the upper lid BUT IT CAN BE REVERSED with special eye drops.
Without insulting your GP - I think he has overstepped his bounds. You need to be examined by a neurologist as it is always possible but not likely that you MAY have a neuromuscular disease (Myasthenia Gravis, Eaton Lambert syndrome) which makes one VERY sensitive to "normal" doses of Botox OR that your LEVATOR or Frontalis were "over" treated.
To have injected you in the orbit from the Crow's feet is unheard of and physically impossible.
Good Luck.

If this occured within two weeks of Botox and there are no other medical reasons then the symptoms should resolve without any residual effects.
Your GP should check the vision and extraoccular muscle movements to make the proper diagnosis.