Can supraorbital and supratrochlear nerve damage heal itself without treatment or medication?

Yes, improvement could indeed occur, but depends upon mechanism of damage and extent of injury. Assuming the nerve is anatomically intact with myelin coverings solely a problem, the time is about 3-4 weeks, but axonal damage recovers at 0.1mm daily, so this could take months. No known medication enhances nerve regrowth.

yes healing is 1 inch/month