Hi
Am I correct in saying that the Database holds only data like my articles, pictures, etc. ?
While the public-html files hold the structure of the site, template, components, modules, plugins, etc. ?
Yes that is a pretty good description as I understand it. The trouble is that over 5000 files go to make up the standard joomla installation and in theory any one of these could have been altered (these are the files in your public_html folder). When my site was hacked I discovered that every index.html file had been changed just to say the site had been hacked (every folder has a blank index.html file!)I was lucky in that scripts etc could have been added instead.
The data base holds all the articles, images, links, scripts that you have added (google maps) etc and you can imagine how difficult and time consuming it would be to check through and identify and foreign additions.
I am sure that your database could be cleaned but it might be expensive.
So rollback to a time when you know the files and database are both secure.
It is a hard learning curve but I bet from now on you will make a regular backup of your site.