I had the exact same problem with the exact same mac (MacBook Pro Retina 13") and, after relying on USB mouse and keyboard, was able to fix it by replacing the trackpad flex cable ( as Reece said one should do).
This is the part I used:
https://www.amazon.com/gp/product/B0711CZPXJ/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
It is a very easy task:
Take off back of computer
Note the ribbon on top of large battery pack in bottom center; this is the flex cable.
Unscrew metal piece covering connector on top end of ribbon, pop connector off.
Peel tape tab on connector on bottom end of ribbon, pull connector out.
Replace with new flex cable (it will be slightly long, so fold it at the edges a bit)
You're done!