I backed up my iPhone onto my computer. I'm not sure if my videos that I filmed personally were backed up, and I don't know where to find the backup on the computer. How can I find these?
The backup is only for use in restoring settings and some content to the iphone.
You should be importing all pics/vids taken with the iphone to your computer regularly as you would with any digital camera.
So is it impossible to view the pictures/videos until I restore them to a new handset?
That is correct.
There are programs that claim they can extract data from iOS backups to be used, but these programs are not endorsed or supported by Apple.
Retrieving data ...