I would like to add special effects that look like live lighting to a photo. Here is an example: ...https://www.facebook.com/Scentsy/videos/10154783783926350/
The problem is that I am a beginner and I am not sure what program to use or plugin or extension that may be needed.
The best program to use for creating lighting effects depends on your image and how you are going to use the final product.
Any program you use will require you to create layers and understand using layers, masking, and blend modes. After Effects is capable of doing more than Photoshop or Premiere Pro but the example you showed could be created in any of these apps.
To start learning AE please Start Here: Basic AE
To get advice on a specific photo please post the photo and explain in detail what you want to do with it.
Thank you for such a prompt answer!