Dropping the phone wouldn’t have helped it much.
The phone had been working for a month after it was fixed, with no apparent problems and the problems started after it was dropped, very coincidental don’t you think?
The best that you can do is to open the phone and check the connection to the display and also inspect for any other obvious internal damage.
I suspect however that the display has been damaged internally and if so, it cannot be repaired. It will have to be replaced.
Here’s the ifixit Samsung Galaxy S III LCD Display/Front Glass Replacement guide that will help.
Replacement displays are available online. Just search for Samsung Galaxy S3 screen replacement