From what you wrote it sounds like your have created a Premiere Elements 13 project file (prel). You have imported files, edited, them and probably saved the project file (prel) to the computer hard drive. What you have just created is just the project file which can be opened in Premiere Elements (same version or a version later than it...none since you have the latest version). It cannot be opened in an earlier version of the program.
But, if you want to watch the edited Timeline content as a movie, then you need to export it under the Publish+Share section of the program. You can export that Timeline to a file (.mov, .wmv, .avi, .mp4....) or burn it to disc (DVD-VIDEO on DVD disc, AVCHD on DVD disc, or Blu-ray disc format on Blu-ray disc). Computer and TV DVD Player and Blu-ray Player possibilities exist for specific type of export.
First thing you need to do is
1. Set up the project correctly so that the project settings match the properties of what you have put on the Timeline.
2. Decide on the export type for you and others to view your export.
The following is a link to the Premiere Elements 13 Help PDF. Please read the section on Saving and Sharing Your Movies using the Publish+Share section of the program.
If you tell me what you have on the Timeline in the way of format (frame size, frame rate, 4:3 or 16:9....), I will customize a mini test run for you to work through.
We will be watching for your reply.