My mesh's automatically deformed in the viewport after aplying a new material to some faces of it I'm new to Blender, and started practicing with Blender Guru's tutorials. I'm currently on the applying a texture part of it. 

I've just finished UV unwrapping using the UV squares addon and just assigned a new, second material to some faces of the cup. Thing is, as soon as I apply the new material, my mesh's pierced everywhere with these 'faces' (sorry, I don't know how to call it). This is shown like this only in the solid viewport, while in Wireframe and Rendered it looks exactly as it is supposed to.

Does anyone know what's happening here? All I can think about is that I screwed up with the unwrapping, or that it may have to do with my PC, I run Blender in a pretty weak machine, though it's been working great up until now, but still, I'm at loss here. Thanks in advance, and sorry for my lack of language in the matter, I'm still a newbie.

I added an image to make it clearer.
while I can't do much without access to the .blend file, from viewing the screenshot it does seem that the strange interior geometry isn't part of the cup object (if it were, it would have edge lines on it since you are in edit mode). I would try leaving edit mode and trying to select it to see if it is a different model. If it is part of the cup, I would try recalculating the cup's normals by pressing "A" to select all faces, then "Alt + N", then selecting "Recalculate Outside" or "Set from Faces". 

I would also check the modifiers tab on the cup and see if you have any displacement or other modifiers which could be causing the effect.