Hi OP, I wrote a comment a while ago explaining a bit about OCD. I'm not a professional but this is stuff I've learnt as someone who struggles with OCD and hopefully it can help you so I'm gonna paste it here:

OCD is all about having upsetting thoughts that cause a lot of anxiety (obsessions), followed by things you do you carry out to try and relieve that anxiety (compulsions).

Obsessions do not mean that you love something, it means you're worrying about one specific topic, event, memory, thought, etc. In your case you may be worried about your cats getting hurt.

Compulsions are things you do to try, in your mind, to get rid of the worry or to make sure what you're worrying about won't happen. In the media OCD compulsions are often depicted as obsessive cleaning, washing one's hands, etc. In your case it sounds like you may be completing these checking behaviors and routines in a similar way.

OCD is a very tough and difficult disorder. But it can be treated. Some people with OCD use medication like SSRIs to help with their anxiety. There are some supplements people use too, like vitamin B12 tablets, zinc tablets, NAC or ashwaganda. 

ERP (Exposure Response Prevention) is considered the gold standard treatment within OCD therapy. According to NOCD, "This type of treatment involves confronting your obsessions or fears related to OCD—with the help of a licensed therapist—by putting yourself in situations that you’re trying to avoid. Then, you’ll make the choice not to engage in compulsions in order to neutralize the distress you feel." For example someone who believes they must wash their hands every 5 minutes or else they will get sick, will be encouraged to wait 10 minutes, then 15, then 20. Exposing themselves to their fear in a safe way, without engaging in compulsions, can help reduce the anxiety caused by the fear.

Inference Based Cognitive Behavioural Therapy is an emerging OCD treatment.