No worries! There shouldn't be a problem using images and other external files; you can push them to GitHub along with your knitted output. For example, this is what my website's repo looks like on GitHub:
I keep my images in the assets folder. If I click on index.html, I can see it that file plain text form:
(Mine has some weird stuff in it, but that's the sort of window you'll get). But if you go to where the repo is hosted (which in my case is my website domain, rensa.co, but in your case will be another address), index.html will be rendered, including any graphics:
The catch is that your image paths (locations) in index.html should be relative: if the image files are in the same folder as index.html, they'll just be filename.jpg or whatever, whereas if they're in a subfolder, like images, they should be something like images/filename.jpg.
Since you didn't write the HTML yourself, that might be a bit hard to check, but if you look at index.html on GitHub (as above) or open it up in a code editor, you can search for HTML image tags, which look like:
<img src="images/pic1.jpg">
If the src attribute in them starts at the root of your computer, like ~/rensa/Code/myproject/images/pic1.jpg, you might have a problem. But if they're just like images/pic1.jpg, and the files are in the right place, it should all work out when you push to GitHub and turn on GitHub Pages 