It seems as though the headphone jack itself may have been damaged.
If this is the case then it cannot be repaired, it has to be replaced.
The easiest option is to replace the IO USB board (supplier example only) as the headphone jack is mounted on the board.
I couldn't find a video that shows how to replace the board but here's a video that shows how to open the laptop so that access to the board is possible.
The board is visible at 1:31 minutes into the video.
Note: To avoid any possible electrical problems from occurring when working inside the laptop, disconnect the battery cable from the motherboard as soon as you can access it before doing anything else. This is shown at 1:34 minutes into the video. You don't have to remove the battery, just disconnect it. Reconnect it last thing after completing the repair, before closing the laptop
If doing this yourself is too daunting, contact a reputable, professional laptop repair service and ask for a quote.