Just wondering, is there any way I can put photos on this thread without using Photobucket or any other program?
No there isn't - and you'll find the same is true of many sites that allow you to display images, they are in fact hosted by a third party. This saves space on the webserver and reduces the amount of bandwidth.
If you don't want to create a Photobucket account, try http://tinypic.com/
which allows you to upload a single image, you don't need an account, and it's free. Hope this helps.