Hi jfsimpson,
We’re happy to provide some assistance.
Given the details you’ve shared, you can only retrieve that photo of your son if you had a backup of your data around the time you accidentally deleted the photo. If you’re unsure if you have a backup of your data from around that time, check out the link below to learn how to locate a backup.
Locate backups of your iPhone, iPad, and iPod touch - Apple Support
If you discover that you have a backup around the time you deleted your son’s photo, you can restore from that backup to retrieve the picture.
You can find how to restore from a backup here: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
Lastly, please keep in mind that restoring from a backup will revert your device back to the date of the backup you restored from. That means you will lose all data after your backup's time and date stamp.
Post back if you still have problems after working through the steps in the link above.
Thanks for using the Apple Support Communities.
Cheers!