If the site lets you load an image from the internet - e.g. gravatar and tinypic both give you that option - then right-click on the picture within a webpage and select the View Image option so that it is displayed in a tab on its own. Then use the URL of that tab.
I believe you misunderstood my question.
I don't want to save the picture before posting it. I want to know if it's possible to upload a picture directly from one website to another website.
If the site lets you load an image from the internet - e.g. gravatar and tinypic both give you that option - then right-click on the picture within a webpage and select the View Image option so that it is displayed in a tab on its own. Then use the URL of that tab.