Okay, I've been trying to figure it out for quite a while now.

In your Hot-link script, if you are considering to allow Google Servers + Your own websites then do not do it because it won't solve your purpose because Google will still keep up to indexing your images from other websites that hot-link your content.

I found a way in just allowing my own website in the script. This would still allow Google to index our images because they access it through our website but a draw-back of doing this is that if other people access it, you can see the images being listed in Google Images but when you click them and select "Full Size Image" you can't access it because at that time, the image is being accessed through Google's Address.

So I wanted a method to fix this ?

Like this is the Google's address of one of my image :

Google's Image Address of my Website

Is there any way we can just allow this URL to access the images in hot-link script for every image, this would fix the need.

You should be able to add a line to your .htaccess file that checks the referer address for an image, and deliver a 403 access denied error if it's not from your own domain.