Has the phone been dropped or gotten wet at all?
If not, how new is “newish”? Less then 12 months?
Check the purchase receipt to verify the purchase date and then check the manufacturer’s warranty documentation that came with the phone.
If the phone is still covered by the manufacturer’s warranty, follow the directions in the warranty as to what to do to make a claim for a manufacturer’s warranty repair, replacement or refund.
If it is no longer covered by the warranty or if it has been dropped or gotten wet, here’s a link to the ifixit Samsung Galaxy S III LCD Display/Front Glass Replacement guide.
This should help you to gain access to the LCD to first check if it may be a loose LCD flex cable connection on the systemboard or if you may need to replace the LCD screen if necessary.
If doing the repair seems to daunting a task, contact a reputable, professional mobile phone repair service and ask for a quote.