Yeah, don't feel bad about the table salt. Seriously my general rule is : don't listen to petstore or fishstore employees, just come to this website instead. LOL!
Now you have the right tools to take care of your betta because you asked for help here.
And for the filter, you still have to do water changes every week (maybe once or twice a week depending on the size of your tank instead of everyday or every other day) and it does help to keep the tank cleaner. If he gets better and you decide to upgrade don't hesitate to ask questions!