I know you said it's not your controller, but does it do it when it's not plugged in? (unplug any controllers you have and load the game, if it's still doing it, you know it's not controller related) What you're describing sounds exactly like a controller where the calibration of an analogue stick isn't quite right.

To calibrate controllers, go to Windows' Control Panel and look for something like "Setup USB Game Controllers" (it varies slightly depending on your version of Windows). When in there you should be able to calibrate it.