It came without screws so it was a quick fix. I just hope it does not hurt anything inside of my PC. I hope that it won't. So far it is running just fine and in fact it is actually running smoother.
No, your computer is completely fine and there is no problem with it! I suggest you find some screws that you can get since you will not want to hold the fan up with duct tape for ever! But no don't worry your computer is completely fine!