Chosen Solution
The DS will register a touch input where there is none in around the same place every time. There is some debris under the plastic near that spot, so I suspect that is causing it. But can I clean the digitizer without ruining the adhesive? There are also a few bubbles under the digitizer (that’s the outermost layer on the bottom screen, right?).
You may need to replace your digitizer. There is a guide here with instructions and you can get a replacement digitizer here or here or here(eBay). I think replacing the digitizer is the best option given the cost.