Porn links added to my site

I am very new to this so I apologise if the solution has been posted in another thread.

I have recently taken over a dance school and thus, the website. We had to recover and reset passwords so that I could log in. After that period I got a message from a student who visited the site and saw porn links scattered throughout the site. However they are only visible for a split second, after which the links disappear and the site looks normal.

After looking through these forums I figured my site may have been hacked during the handover phase maybe, so I changed the passwords and updated to version 4.1. I also searched all the pages code, using keywords that were in the disappearing links but I couldn’t find anything obviously out of the ordinary, but there is still lots of code I do not understand there so I could easily have missed something.

Does this sound familiar to anyone? What should I be doing next to fix this?

The site is http://www.swingzing.com

I also managed to get screen shots when the links were visible and after the disappeared. If they may help let me know.

Thanks