While trying to make a new armor piece, I cant find any textures to put in the Biped Model, World Model, Icon Image, and Message Icon boxes. I have uninstalled and reinstalled Fallout 3 about 3 times to put it in the right place, would that have any effect on my problem?

You can find all of the game's textures inside the BSA files in which they are stored.
If you already know the filename(s) you need, you can use FO3edit to type in those values without opening the BSA up.

BSA tools can be found in Fallout Mod Manager (FoMM for Short)

Ahh, was wondering why everyone recommended getting FoMM. Thanks