Several things are wrong.
* Your HTML needs to be consistent. Some h3's are within their own div, with their content in a separate div, while others are siblings to their content. You need the latter with the code originally provided.
* Some h3's contain anchors which will receive the click event and probably go to the top of the page.
* The select #h3 looks for an element with an ID of h3, whereas you want to select all h3 elements. Use the original code, changing h4 to h3.
* You have hard-coded a content div to slide out (#hmg_provider_search_specialty_more), rather than using the one relative to the currently clicked header. Use the original code that references this.