OK, lets assume that this is a graphics driver problem or a VSync one. Do these:
Download Driver Sweeper
and install it. Do not run it yet.
Uninstall the AMD drivers and all of their components.
Now run Driver Sweeper. Select all GPU traces (ATI, AMD) and delete whatever GPU-related is found.
Reboot your system and then download THIS
(Catalyst 11.6, do not use the latest beta or something else).
After installation reboot your system again. Make sure that in device manager your AMD card appears.
Do a file integrity check from Steam again making sure the game is fully updated.
Since you are at the beginning, delete all your current progress(just to be sure the problem is not there) by deleting the folder Amnesia inside Documents (your settings and game progress will be lost).
Start the game. At Options menu make sure VSync is disabled and start a new game.
It should work after all these. They are actually 3-4 solutions mixed up together.