Well honestly I think the best thing to do is to just stay away from cats as much as possible so you don't get the urge. But that would be hard to do especially if your girlfriend has so many.

There is no known mental illness that fits what your describing that I know of. Are you able to control your urges? And as far as 'self-help' goes I think you should try and explore why you feel like you need to harm cats. What do you feel when your around them? How do you feel about the cat? Does anything trigger the need apart from seeing a cat? And how do you imagine feeling if you actually harmed the cat? Try and put these pieces together…

But if you ever do seriously harm a cat, it's something you can never take back. You will regret it very much I'm sure and it will mess with your self identity of who you are as a person. If you consider yourself a decent human being.

If therapy is not an option try and find ways to distract yourself when your around cats and try and relax your mind when you feel the impulse to hurt them.