Can you talk with a therapist about it? The thing about OCD is that it gets worse everytime you give into your impulses. I don't have OCD but I sometimes get into spirals of intrusive thoughts, during which I start believing irrational things too, for example that a thought about my health will manifest if I keep thinking it. I know it's irrational, so I understand how you felt about the cat too. Whenever I get a negative thought, I whisper "7-9-13" to myself, and when it's bad I do it three times in a row to make sure it worked. 😅 The difference is that I manage to get myself out of these spirals too – at least to a large extend – but it can be incredibly difficult; I find that I have to alter my personality and become a person who doesn't fear death, just in order to break the pattern. Lately I was able to stop myself from whispering my silly numbers, but I still do it from time to time, especially if the intrusive thought was about someone else (then I feel like I can't run the risk). If you wanted to, you could start by giving up taking pictures of the doors, but I don't know how hard that would be for you. If I was you I would definitely take it seriously because it can potentially get to a point where it takes up your whole life. I only understand it to some degree myself, but I think therapy treatment can be effective if the therapist specializes in anxiety disorders.

He doesn't have rabies.

Sick cats are targets for prey... so, they typically withdraw and hide to recover. He's still approaching you, so he doesn't have rabies.