OK, do you have a copy of your manual?
When in the Camera application, and you click on Settings, do you have the pictures being saved to the SD Card (if you have one), or Internal Storage? (Pages 46, 46, 47)
Now then, have you used Gallery? (Pages 48, 49, 52, 53, 54)
Hopefully, using the Gallery, you'll find them.
You can install a microSD card in your phone up to 32GB in size. A 16GB card might cost just under $10, and a 32GB perhaps $15-20. They are sold on Amazon, Target, BestBuy.
I would consider getting one, and setting the camera to store the images and videos you take there.