如何检查某人是否在Facebook上分享了我的网页?

I can check shares like this

https://graph.facebook.com/?id=http://amazon.com

this will give me a response like

{
   "id": "http://amazon.com",
   "shares": 1395576,
   "comments": 14
}

Now, after a user has clicked on share button I can again call

https://graph.facebook.com/?id=http://amazon.com

and if share count has increased I will know it has been shared. Is there any other better way?

You can direct the json data display on a web page

You can´t, and this is intended - because it would be able to gate content behind a Share Button, which is not allowed according to the platform policy:

4.5 Only incentivize a person to log into your app, enter a promotion on your app’s Page, or check-in at a place. Don’t incentivize other actions.