Best I can suggest is to let it cool properly (turning it off will help) then see whether it's any better.
If the digitizer has actually been damaged then you'll need it replaced. But I've never heard of this before -I guess it must have got very hot! Maybe, just maybe, a connector has been partially disconnected, but I think that's unlikely (though cheaper if that's it - push it in properly and it's fixed).
If you still have a warranty you could get it fixed that way.