When you said the mouse moves faster the longer you move it, it made me think of the "Enhance pointer precision" option in Windows, and the "Mouse Smoothing" option often found in games.
Check to see if these options are enabled. The first option can be found by going to the Windows Control Panel, opening the Mouse settings and click the "Pointer Options" tab. The option is in there.
There's an option in Amnesia called "Smooth Mouse" which might also be worth switching off, at least to see if it helps. You can get to this option by going to the in-game options menu, and then selecting the Input tab.
If neither of those tweaks works I'm not sure what else to suggest. If the problem persists post again and maybe someone else can chime in