I'm sorry but your DM is right, what you did is evil. Resorting to lethal force immediately after getting a scratch is not good or even neutral behavior. It's compounded by the fact that (a) you knew the cat was sapient and (b) you had reason to believe it wasn't evil (i.e. because it was inside the evil-blocking barrier.)

Even if you suspected it was an infiltrator that had somehow penetrated the barrier, you have no concrete evidence of that and thus your use of force was excessive. Hell, even if you had detected its alignment as evil (which you didn't), lethal force is still an immoral response unless the cat is about to inflict imminent harm on yourself or someone else.

The fact that you even knew about the barrier makes your actions not just immoral, but not very well thought out either. If I was inside a barrier like that I wouldn't even swat a fly until I left.