I shared a Listing I created on Facebook, then I went and changed the price and tried to re-share that Listing BUT Facebook is still showing the old price. 

The reason that the old price is still showing is because FB caches everything, or maybe more accurately, SUPER CACHES EVERYTHING.

That being said, once you post a URL or something similar, Facebook automatically saves whatever the first instance on that URL is, so when you change a detail on that URL Facebook will not notice it.

To fix this, you have to re-scrape your Facebook page (basically the equivalent of clearing your cache but for Facebook alone).

To re-scrape your Facebook, go to the following link:

Drop in the URL you are having issues with in the box provided. 

Click 'Debug'

You can see the Time Scraped (the first time you shared that URL on Facebook)

The Link Preview, etc. 

At the very top, where you see the Time Scraped, hit 'Scrape Again'

You should then see your updated Time Scraped AND your updated Link Preview!

For more information on how to re-scrape your Facebook check out this link: