Ok. When you create a texture, you need to UV the model, which means take the 3d model, and unwrap it in a way so that it fits into a 2d space. You then create a UV snapshot, which exports a black and white image that shows your unwrapped model. When you bring this into Photoshop and start texturing, you use these lines as guides as to where you should place/paint your textures. You need to allow about 1 or 2 pixels past these lines, due to filtering (not really important for your case, but still expand the edges) Upon final export of your texture, you need to make sure that you turn off the UV snapshot inside your Photoshop document.

Are those images from Maya, or from the game engine? If it's from the game engine, grab your UV's and shrink them a bit in width. The engine may be having problems at the textures bounds.