Never had a problem with my neons funkyfish and they're in with guppies (they don't even seem to eat many of the new fry)
Bettas can be unpredictable and aggressive to other fish in their tank......they all have different personalities. Does the cory have somewhere to shelter in the tank i.e a cave, pipe, somewhere the betta can't see him/get him cornered.
Fish are fine with one eye though your little cory is not going to be able to protect himself and will be more vulnerable now, especially on the blindside. Watch the fish and see if you can see who is chasing whom......long term you may need to separate the chaser out into a different tank.
I don't medicate unless I need to .....if the eye socket looks ok I'd be checking him daily, making sure the water quality was good, providing loads of places for him to hang out (extra plants/ornaments) and feeding high quality diet (adding live/frozen foods to his normal diet)
Good luck with the cory and let us know how you get on
sue