I use a HDD with ubuntu 12.04 on it for school, and when i do school related work I plug it on my PC and work on it, but I've found some problems and i think its due to the graphics drivers, I installed the nvidia ones for my PC, but the school PC has integrated graphic chipset, so i would need different drivers. Can I install both on the same ubuntu system without causing driver conflicts or something?
Yes, you can install multiple drivers. When Ubuntu boots, it looks for what hardware works, then chooses matching drivers. Even if
lspci | grep "Display\VGA" shows a non-Nvidia integrated graphics controller, you can add the non-nVidia driver.