Send it off to Nintendo, l wouldnt risk a phone type place - they buggered up our young uns iPhone with the glue they use. Nintendo seem to be reasonable, they ask to send in controllers if they've been affected by the drift problem and sort free of charge
Can you tell if it’s the lcd screen or just the digitiser that is broken? Changed screens on kids iPads loads of times when they were young uns and it was usually just the front digitiser screen that got broken.