It's not possible to place a character or an image at the end of a paragraph automatically by using a paragraph style.
It's possible that it could be accomplished by a script, but I don't write scripts.
Actually it is, if the image is simple enough to be converted to a one-character font. I think the OP found this technique in another thread and posted so in the duplicate of this one that Jive has kindly provided....
And if it's just that square bullet, you probably don't even need a custom font, just add the glyph with the correct Unicode position to match the box in a symbol font like WingDings or Zapf Dingbats.
Changing the character is then as simple as defining a character style to assign the symbol font and any scaling required and adding a GREP style: .\Z finds the last character in a story.
Yes, I was reading from the earlier posting. Jive has been playing tricks again.