Hi Shelly. Don't panic once you find that the photo loss happened. The first thing I hope you can do is to stop using the device to avoid the data overwritten situation. Actually the delete command or formatting will not really delete the files in your device. All the commands do is only to free up the space of the deleted files so that the space can be used by the new files. If you keep operating on your device, you may make some new files which will take the space of the deleted files and you will lose the chances to recover the deleted files.
To help you to solve your problems, you need to make your son's Nintendo DSi as a USB drive or external drive which can be read by the computer and then search methods to recover the files. You can check more details in this post to get more helpful tips you may need: http://www.uflysoft.com/data-recovery-mac/how-to-recover-data-from-usb.html