@datboilizzy I don't have a tower because I have a laptop and use an external disk drive but if it's any help I installed Sims 3 yesterday and it was quite noisy but I don't think it's anything to worry about. It's just working hard to read the disk.
I haven't used a tower in a while but I believe they have preventative methods to avoid overheating. I remember mine had ventilation issues and the whole thing would force-shut off if it got too hot to prevent any damage.
When you say shake, do you mean like you can see it moving from the vibrations or like it's actually shaking from side to side wobbling?
Also just ensure there is plenty of room around the ventilation vents so that there's plenty of space for air to come out and go in. Also check if the fans are clogged up with dust. If it is getting unusually hot, it may be worth checking.