No it's not a fixed size in a picture. It's essentially one dot (Picture Element) in the picture. So a 800x600 picture is 800 dots wide by 600 dots high. Since you can zoom in and out on a picture, and it's size on the screen will change, yet the pixels won't - it follows that a pixel (in a picture) is not a fixed size.
Can you explain why you need to resize your pictures, then a better explanation of what you should do can be suggested.